DP Mathematics HL Questionbank

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• 16M.2.hl.TZ2.8b: Using an appropriate sketch graph, find the particle’s displacement when its acceleration is...
• 16M.2.hl.TZ2.8a: Find the particle’s acceleration in terms of \(s\).
• 16M.2.hl.TZ1.3c: Find the acceleration of the particle at time \(t = 0\).
• 16M.2.hl.TZ1.3b: Find an expression for the acceleration, \(a\), of the particle at time \(t\).
• 16M.2.hl.TZ1.3a: Find an expression for the velocity, \(v\), of the particle at time \(t\).
• 17N.1.hl.TZ0.5: A particle moves in a straight line such that at time \(t\) seconds \((t \geqslant 0)\), its...
• 12M.2.hl.TZ2.12c: (i)     Write down the time T at which the velocity is zero. (ii)     Find the distance...
• 12M.2.hl.TZ2.12d: Find an expression for s , the displacement, in terms of t , given that s = 0 when t = 0 .
• 12M.2.hl.TZ2.12e: Hence, or otherwise, show that \(s = \frac{1}{2}\ln \frac{2}{{1 + {v^2}}}\).
• 12N.2.hl.TZ0.6: A particle moves along a straight line so that after t seconds its displacement s , in...
• 08M.2.hl.TZ2.13: A particle moves in a straight line in a positive direction from a fixed point O. The velocity v...
• 11M.2.hl.TZ2.3b: How far above the ground is she 10 seconds after jumping?
• 11M.2.hl.TZ2.3a: Find her acceleration 10 seconds after jumping.
• SPNone.2.hl.TZ0.5a: Given that P is at the origin O at time t = 0 , calculate (i)     the displacement of P from O...
• SPNone.2.hl.TZ0.5b: Find the time at which the total distance travelled by P is 1 m.
• 13M.2.hl.TZ1.12e: A second particle, B, moving along the same line, has position \({x_B}{\text{ m}}\), velocity...
• 13M.2.hl.TZ1.12d: At t = 0 the particle is at point O on the line. Find an expression for the particle’s...
• 13M.2.hl.TZ1.12f: Find the value of t when the two particles meet.
• 10M.2.hl.TZ1.14: A body is moving through a liquid so that its acceleration can be expressed...
• 10N.1.hl.TZ0.12a: A particle P moves in a straight line with displacement relative to origin given...
• 13M.2.hl.TZ2.10: The acceleration of a car is \(\frac{1}{{40}}(60 - v){\text{ m}}{{\text{s}}^{ - 2}}\), when its...
• 11M.2.hl.TZ1.8a: Find an expression for the acceleration of the jet plane during this time, in terms of \(t\) .
• 11M.2.hl.TZ1.8b: Given that when \(t = 0\) the jet plane is travelling at \(125\) ms−1, find its maximum velocity...
• 11M.2.hl.TZ1.8c: Given that the jet plane breaks the sound barrier at \(295\) ms−1, find out for how long the jet...
• 18M.2.hl.TZ2.7b.ii: Find the value of the acceleration of P at time t1.
• 18M.2.hl.TZ2.7b.i: Find an expression for the acceleration of P at time t.
• 18M.2.hl.TZ2.7a: Determine the first time t1 at which P has zero velocity.
• 14M.1.hl.TZ1.8: A body is moving in a straight line. When it is \(s\) metres from a fixed point O on the line its...
• 14M.2.hl.TZ2.14d: Find the acceleration of particle B when \(s = 0.1{\text{ m}}\).
• 14M.2.hl.TZ2.14c: Find the exact distance travelled by particle \(A\) between \(t = 0\) and \(t = 6\)...
• 15M.2.hl.TZ1.13d: You are told that Richard’s acceleration, \(a(t) =  - 10 - 5v\), is always positive, for...
• 15N.2.hl.TZ0.9b: (i)     Find the time \(t < {t_2}\) when the particle has a maximum velocity. (ii)     Find...
• 15M.2.hl.TZ1.13a: (i)     Find his acceleration \(a(t)\) for \(t < 10\). (ii)     Calculate \(v(10)\). (iii)  ...
• 15M.2.hl.TZ1.13f: You are told that Richard’s acceleration, \(a(t) =  - 10 - 5v\), is always positive, for...
• 15M.2.hl.TZ1.13c: You are told that Richard’s acceleration, \(a(t) =  - 10 - 5v\), is always positive, for...
• 15M.2.hl.TZ1.13e: You are told that Richard’s acceleration, \(a(t) =  - 10 - 5v\), is always positive, for...
• 15N.2.hl.TZ0.9a: Write down the first two times \({t_1},{\text{ }}{t_2} > 0\), when the particle changes...
• 15M.2.hl.TZ1.13b: At \(t = 10\) his parachute opens and his acceleration \(a(t)\) is subsequently given by...
• 15M.2.hl.TZ2.12a: Find the displacement of the particle when \(t = 4\).
• 15M.2.hl.TZ2.12c: For \(t > 5\), the displacement of the particle is given by...
• 15M.2.hl.TZ2.12b: Sketch a displacement/time graph for the particle, \(0 \le t \le 5\), showing clearly where the...
• 15M.2.hl.TZ2.12d: For \(t > 5\), the displacement of the particle is given by...
• 14N.2.hl.TZ0.8b: The particle returns to its initial position at \(t = T\). Find the value of T.
• 14N.2.hl.TZ0.8a: Find the value of \(t\) when the particle is instantaneously at rest.