Physics 1 · Problem Set 42
2. (continued) Sketch the car's velocity against time for the first ten seconds, and mark on your sketch the moment its acceleration changes sign.
3. A ball is thrown straight up from a balcony. Its height above the ground after t seconds is
h(t) = −5t2 + 20t + 1 (metres)
(a) When does the ball reach its highest point?
(b) How high does it go?
(c) With what speed does it pass the balcony again on the way down?
4. A cyclist coasts to rest on level ground. Her speed after t seconds is v(t) = 12 − 1.5t metres per second. How far does she travel before she stops?
5. Explain in one sentence why the area under a velocity–time graph gives the distance travelled.

