DP Mathematics SL Questionbank
Kinematic problems involving displacement \(s\), velocity \(v\) and acceleration \(a\).
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[N/A]Directly related questions
- 18M.2.sl.TZ2.9e: Find the total distance travelled by P.
- 18M.2.sl.TZ2.9d: Find the acceleration of P when it changes direction.
- 18M.2.sl.TZ2.9c: Write down the number of times that the acceleration of P is 0 m s−2 .
- 18M.2.sl.TZ2.9b: Find the maximum speed of P.
- 18M.2.sl.TZ2.9a: Find the initial velocity of P.
- 18M.2.sl.TZ1.10b.ii: For the graph of \(f\), write down the period.
- 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.TZ1.10d: Find the maximum speed of the ball.
- 18M.2.sl.TZ1.10c: Hence, write \(f\left( x \right)\) in the form \(p\,\,{\text{cos}}\,\left( {x + r} \right)\).
- 18M.2.sl.TZ1.10b.i: For the graph of \(f\), write down the amplitude.
- 18M.2.sl.TZ1.10a: Find the coordinates of A.
- 17N.2.sl.TZ0.9d: Find the total distance travelled by P when its velocity is increasing.
- 17N.2.sl.TZ0.9c: Find an expression for the velocity of P at time \(t\).
- 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.TZ0.9a: Write down the values of \(t\) when \(a = 0\).
- 16M.2.sl.TZ2.7: A particle moves in a straight line. Its velocity \(v{\text{ m}}\,{{\text{s}}^{ - 1}}\) after...
- 16M.2.sl.TZ1.9e: Find the maximum speed of P.
- 16M.2.sl.TZ1.9d: Find the acceleration of P after 3 seconds.
- 16M.2.sl.TZ1.9c: Write down the number of times P changes direction.
- 16M.2.sl.TZ1.9b: Find when P is first at rest.
- 16M.2.sl.TZ1.9a: Find the displacement of P from O after 5 seconds.
- 16N.2.sl.TZ0.9d: (i) Find the total distance travelled by P between \(t = 1\) and \(t = p\). (ii) Hence...
- 16N.2.sl.TZ0.9c: (i) Find the value of \(q\). (ii) Hence, find the speed of P when \(t = q\).
- 16N.2.sl.TZ0.9b: Find the value of \(p\).
- 16N.2.sl.TZ0.9a: Find the initial velocity of \(P\).
- 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.TZ1.4b: Write down the value of t when the velocity is greatest.
- 09M.1.sl.TZ1.4a: Complete the following table by noting which graph A, B or C corresponds to each function.
- 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.TZ1.10b(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.TZ1.10a: Write down the velocity of the particle when \(t = 0\) .
- 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 \(0\).
