PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials
Problem
A driver is guiding a car along a straight, level road. The motion is recorded by an onboard computer that can report the car’s instantaneous velocity v(t) (in m/s) and instantaneous acceleration a(t) (in m/s2) at any clock time t (in s).
(a) Describe, in complete sentences, the conditions on v(t) and a(t) that must be satisfied at an instant t=c for the car’s speed to be (i) increasing and (ii) decreasing at that moment.
(b) At t=3s the computer records v(3)=−4m/s and a(3)=−1.2m/s2. Determine whether the car’s speed is increasing or decreasing at t=3s and explain your reasoning clearly in terms of the signs you found in part (a).
(c) Provide one concrete numerical example (that differs from part (b)) in which the car has negative velocity but its speed is decreasing. State the values of v and a, verify the required sign pattern, and explain briefly why these values lead to decreasing speed.