Fig. 1 shows a velocity-time graph for an electric delivery van travelling along a level road. The van accelerates from a depot, travels at a steady speed, ...
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Fig. 1 shows a velocity-time graph for an electric delivery van travelling along a level road. The van accelerates from a depot, travels at a steady speed, then brakes at a junction. Its mass, including parcels, is 1200 kg. A student uses the graph to calculate the force needed during the first part of the journey. Ignore air resistance during this calculation.
(a) State what is represented by the gradient of a velocity-time graph. [1]
(b) Calculate the acceleration of the van during the first 8 s. [2]
(c) Calculate the distance travelled by the van during the first 20 s. [3]
(d) Calculate the resultant force on the van during the first 8 s. [2]
(e) Describe the motion of the van between 8 s and 20 s. [2]
(f) Explain why the resultant force is zero between 8 s and 20 s, even though the motor may still transfer energy. [3]
(g) State the SI unit of force. [1]
Answer Details
(a) The gradient of a velocity-time graph represents acceleration. [1]
(b)
\[a=\frac{12-0}{8}=1.5\text{ m/s}^2\]
[2]
(c) Distance is the area beneath the velocity-time graph.
\[\text{triangle}=\frac12\times8\times12=48\text{ m}\]
\[\text{rectangle}=12\times12=144\text{ m}\]
\[\text{total}=48+144=192\text{ m}\]
[3]
(d)
\[F=ma=1200\text{ kg}\times1.5\text{ m/s}^2=1800\text{ N}\]
[2]
(e) Between 8 s and 20 s, the van travels at constant velocity, 12 m/s. [2]
(f) Constant velocity means zero acceleration. By \(F=ma\), zero acceleration means zero resultant force. The motor can still transfer energy because its driving force balances resistive forces, such as air resistance and tyre friction. [3]
(g) The SI unit of force is the newton, N. [1]
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