Question

A cyclist moving with a constant velocity of 6.0 m/s forward passes a car that is just starting. If the car has a constant acceleration of 2.0 m/s2, when will the car overtake the cyclist?

Answer 1

After 6 seconds, the car will surpass the cyclist.

Explanation:

The speed of the cyclist = 6 m/s.

Let after time t sec, the car will overtake the cyclist.

So, distance covered by the cyclist in t sec = 6t m

Initial velocity of the car is 0 m/s, because the car is just starting.

Acceleration of the car =$2 m/s^2$.

Final velocity of the car =6 m/s.

So to cover the distance 6t, the time required by the car = $\frac{1}{2} \times a \times t^2 = \frac{1}{2} \times 2 \times t^2$

$6t = \frac{1}{2} \times 2 \times t^2\\6t = t^2$

t =6 sec

So, after 6 seconds, the car will surpass the cycle.