Paper 2 Kinematics Drills

Q1 Straight-line motion graph

The velocity-time graph for a small trolley moving along a straight track is described as follows.

• From $t=0$ to $t=4.0\mathrm{s}$, velocity increases uniformly from $0$ to $8.0\mathrm{m}{\mathrm{s}}^{-1}$.
• From $t=4.0\mathrm{s}$ to $t=10.0\mathrm{s}$, velocity is constant at $8.0\mathrm{m}{\mathrm{s}}^{-1}$.
• From $t=10.0\mathrm{s}$ to $t=14.0\mathrm{s}$, velocity decreases uniformly to $-4.0\mathrm{m}{\mathrm{s}}^{-1}$.

1. State what the gradient of a velocity-time graph represents. [1]
2. Calculate the acceleration during the first $4.0\mathrm{s}$. [2]
3. Calculate the displacement of the trolley from $t=0$ to $t=14.0\mathrm{s}$. [3]
4. Explain why the distance travelled is not equal to the displacement in this case. [2]

Q2 Vertical motion

A ball is thrown vertically upwards from a balcony with speed $14.0\mathrm{m}{\mathrm{s}}^{-1}$. The balcony is $18.0\mathrm{m}$ above the ground. Air resistance is negligible. Take upward as positive and $g=9.81\mathrm{m}{\mathrm{s}}^{-2}$.

1. State the acceleration of the ball during its flight. [1]
2. Calculate the time taken for the ball to reach its highest point. [2]
3. Calculate the maximum height of the ball above the balcony. [2]
4. Show that the time taken to reach the ground is about $4.1\mathrm{s}$. [3]
5. Calculate the velocity of the ball just before it reaches the ground. [2]

Q3 Falling with air resistance

A skydiver falls vertically from rest. Before the parachute opens, the motion can be described qualitatively using weight and air resistance.

1. Explain why the skydiver’s acceleration is initially close to $g$. [2]
2. Explain why the acceleration decreases as the speed increases. [3]
3. State the condition for terminal velocity. [1]
4. Sketch, on labelled axes, a velocity-time graph for the motion from rest until terminal velocity is reached. [3]
5. Explain why the graph should approach terminal velocity gradually rather than reach it by a sharp corner. [2]