DP Mathematics SL Questionbank

• Syllabus

6.6

Sub sections and their related questions

Kinematic problems involving displacement $s$, velocity $v$ and acceleration $a$.

• 12N.2.sl.TZ0.7a: On the grid below, sketch the graph of $s$ .
• 12N.2.sl.TZ0.7b: Find the maximum velocity of the particle.
• 12M.2.sl.TZ2.5a: Find the acceleration of the particle after 2.7 seconds.
• 12M.2.sl.TZ2.5b: Find the displacement of the particle after 1.3 seconds.
• 08N.1.sl.TZ0.9a: Find the acceleration of the particle at $t = 0$ .
• 08N.1.sl.TZ0.9b: Find the velocity, v, at time t, given that the initial velocity of the particle is...
• 08N.1.sl.TZ0.9c: Find $\int_0^3 {v{\rm{d}}t}$ , giving your answer in the form $p - q\cos 3$ .
• 08N.1.sl.TZ0.9d: What information does the answer to part (c) give about the motion of the particle?
• 08M.1.sl.TZ1.6: A particle moves along a straight line so that its velocity, \(v{\text{ m}}{{\text{s}}^{ -...
• 12M.1.sl.TZ1.10a: Find $s'(t)$ .
• 12M.1.sl.TZ1.10b: In this interval, there are only two values of t for which the object is not moving. One value is...
• 12M.1.sl.TZ1.10c: Show that $s'(t) > 0$ between these two values of t .
• 12M.1.sl.TZ1.10d: Find the distance travelled between these two values of t .
• 09M.1.sl.TZ1.4a: Complete the following table by noting which graph A, B or C corresponds to each function.
• 09M.1.sl.TZ1.4b: Write down the value of t when the velocity is greatest.
• 09M.1.sl.TZ2.11a: (i)     If $s = 100$ when $t = 0$ , find an expression for s in terms of a and t. (ii)    If...
• 09M.1.sl.TZ2.11b: A train M slows down so that it comes to a stop at the station. (i)     Find the time it takes...
• 09M.1.sl.TZ2.11c: For a different train N, the value of a is 4. Show that this train will stop before it reaches...
• 10M.2.sl.TZ1.6: The acceleration,  $a{\text{ m}}{{\text{s}}^{ - 2}}$, of a particle at time t seconds is given...
• SPNone.1.sl.TZ0.3a: Write down the car’s velocity at $t = 3$ .
• SPNone.1.sl.TZ0.3b: Find the car’s acceleration at $t = 1.5$ .
• 11M.1.sl.TZ1.10a: Write down the velocity of the particle when $t = 0$ .
• 11M.1.sl.TZ1.10b(i) and (ii): When $t = k$ , the acceleration is zero. (i)     Show that $k = \frac{\pi }{4}$ . (ii)   ...
• 11M.1.sl.TZ1.10c: When $t < \frac{\pi }{4}$ , $\frac{{{\rm{d}}v}}{{{\rm{d}}t}} > 0$ and when...
• 11M.1.sl.TZ1.10d(i) and (ii): Let d be the distance travelled by the particle for $0 \le t \le 1$ . (i)     Write down an...
• 11M.1.sl.TZ2.9a: Write down $f(x)$ in the form $f(x) = - 10(x - p)(x - q)$ .
• 11M.1.sl.TZ2.9b: Find another expression for $f(x)$ in the form $f(x) = - 10{(x - h)^2} + k$ .
• 11M.1.sl.TZ2.9c: Show that $f(x)$ can also be written in the form $f(x) = 240 + 20x - 10{x^2}$ .
• 11M.1.sl.TZ2.9d(i) and (ii): A particle moves along a straight line so that its velocity, $v{\text{ m}}{{\text{s}}^{ - 1}}$...
• 13M.1.sl.TZ2.6: A rocket moving in a straight line has velocity $v$ km s–1 and displacement $s$ km at time...
• 14M.2.sl.TZ1.6: Ramiro and Lautaro are travelling from Buenos Aires to El Moro. Ramiro travels in a vehicle...
• 14M.2.sl.TZ2.9a: Find the velocity of the particle when $t = 1$.
• 14M.2.sl.TZ2.9b: Find the value of $t$ for which the particle is at rest.
• 14M.2.sl.TZ2.9c: Find the total distance the particle travels during the first three seconds.
• 14M.2.sl.TZ2.9d: Show that the acceleration of the particle is given by $a = 6t{({t^2} - 4)^2}$.
• 14M.2.sl.TZ2.9e: Find all possible values of $t$ for which the velocity and acceleration are both positive...
• 13N.2.sl.TZ0.5c: Find the velocity of the particle when its acceleration is zero.
• 14N.2.sl.TZ0.7a: Find the distance travelled by the particle for $0 \le t \le\ \frac{\pi }{2}$.
• 15N.2.sl.TZ0.6a: Find the value of $t$ when the particle is at rest.
• 15N.2.sl.TZ0.6b: Find the value of $t$ when the acceleration of the particle is $0$.
• 16M.2.sl.TZ1.9a: Find the displacement of P from O after 5 seconds.
• 16M.2.sl.TZ1.9b: Find when P is first at rest.
• 16M.2.sl.TZ1.9c: Write down the number of times P changes direction.
• 16M.2.sl.TZ1.9d: Find the acceleration of P after 3 seconds.
• 16M.2.sl.TZ1.9e: Find the maximum speed of P.
• 16M.2.sl.TZ2.7: A particle moves in a straight line. Its velocity $v{\text{ m}}\,{{\text{s}}^{ - 1}}$ after...
• 16N.2.sl.TZ0.9a: Find the initial velocity of $P$.
• 16N.2.sl.TZ0.9b: Find the value of $p$.
• 16N.2.sl.TZ0.9c: (i)     Find the value of $q$. (ii)     Hence, find the speed of P when $t = q$.
• 16N.2.sl.TZ0.9d: (i)     Find the total distance travelled by P between $t = 1$ and $t = p$. (ii)     Hence...
• 17N.2.sl.TZ0.9a: Write down the values of $t$ when $a = 0$.
• 17N.2.sl.TZ0.9b: Hence or otherwise, find all possible values of $t$ for which the velocity of P is decreasing.
• 17N.2.sl.TZ0.9c: Find an expression for the velocity of P at time $t$.
• 17N.2.sl.TZ0.9d: Find the total distance travelled by P when its velocity is increasing.
• 18M.2.sl.TZ1.10a: Find the coordinates of A.
• 18M.2.sl.TZ1.10b.i: For the graph of $f$, write down the amplitude.
• 18M.2.sl.TZ1.10c: Hence, write $f\left( x \right)$ in the form $p\,\,{\text{cos}}\,\left( {x + r} \right)$.
• 18M.2.sl.TZ1.10d: Find the maximum speed of the ball.
• 18M.2.sl.TZ1.10e: Find the first time when the ball’s speed is changing at a rate of 2 cm s−2.
• 18M.2.sl.TZ1.10b.ii: For the graph of $f$, write down the period.
• 18M.2.sl.TZ2.9a: Find the initial velocity of P.
• 18M.2.sl.TZ2.9b: Find the maximum speed of P.
• 18M.2.sl.TZ2.9c: Write down the number of times that the acceleration of P is 0 m s−2 .
• 18M.2.sl.TZ2.9d: Find the acceleration of P when it changes direction.
• 18M.2.sl.TZ2.9e: Find the total distance travelled by P.

Total distance travelled.

• 08N.1.sl.TZ0.9a: Find the acceleration of the particle at $t = 0$ .
• 08N.1.sl.TZ0.9b: Find the velocity, v, at time t, given that the initial velocity of the particle is...
• 08N.1.sl.TZ0.9c: Find $\int_0^3 {v{\rm{d}}t}$ , giving your answer in the form $p - q\cos 3$ .
• 08N.1.sl.TZ0.9d: What information does the answer to part (c) give about the motion of the particle?
• 12M.1.sl.TZ1.10c: Show that $s'(t) > 0$ between these two values of t .
• 12M.1.sl.TZ1.10d: Find the distance travelled between these two values of t .
• 10N.2.sl.TZ0.2a: On the grid below, sketch the graph of v , clearly indicating the maximum point.
• 10N.2.sl.TZ0.2b(i) and (ii): (i)     Write down an expression for d . (ii)    Hence, write down the value of d .
• SPNone.1.sl.TZ0.3c: Find the total distance travelled.
• 11N.2.sl.TZ0.7a: Find $v(t)$ , giving your answer in the form $a{(t - b)^2} + c$ .
• 11N.2.sl.TZ0.7b: A particle moves along a straight line so that its velocity in ms−1 , at time t seconds, is given...
• 11M.1.sl.TZ1.10a: Write down the velocity of the particle when $t = 0$ .
• 11M.1.sl.TZ1.10b(i) and (ii): When $t = k$ , the acceleration is zero. (i)     Show that $k = \frac{\pi }{4}$ . (ii)   ...
• 11M.1.sl.TZ1.10c: When $t < \frac{\pi }{4}$ , $\frac{{{\rm{d}}v}}{{{\rm{d}}t}} > 0$ and when...
• 11M.1.sl.TZ1.10d(i) and (ii): Let d be the distance travelled by the particle for $0 \le t \le 1$ . (i)     Write down an...
• 13M.2.sl.TZ1.5b.ii: Write down the positive $t$-intercept.
• 14M.2.sl.TZ2.9b: Find the value of $t$ for which the particle is at rest.
• 13N.2.sl.TZ0.5b: Find the distance travelled by the particle in the first three seconds.
• 14N.2.sl.TZ0.7a: Find the distance travelled by the particle for $0 \le t \le\ \frac{\pi }{2}$.