Motorcyclist A travelling at 36 km/h applies the brakes and stops the vehicle in 10 s. motorcyclist B travelling at 18 km/h applies the brakes and stops the vehicle in 20 s. Plot speed-time graph for A and B. which vehicle traveled farther before it came to a stop?

For motorist A,

Initial velocity = 36 km/h = 36 × (5/18) = 10 m/s

Time of stop = 10 s

Using,

v² = u² + 2as

=> v² = u² + 2(v - u)s/t

=> 0 = 10² + 2(0 - 10)s/10

=> s = 50 m

And for the motorist B,

Initial velocity = 18 km/h = 18 × (5/18) = 5 m/s

Time of stop = 20 s

Using,

v² = u² + 2as

=> v² = u² + 2(v - u)s/t

=> 0 = 5² + 2(0 - 5)s/20

=> s = 50 m

Thus, both A and B cover equal distance before coming to rest.

For the speed time graph we need the speed time equation. Which are as follows:

For motorist A, a = (v - u)/t

=> a = -10/10 = -1 m/s²

Time varies from t = 0 s to t = 10 s and the equation is: v = 10 - t

For motorist B, a = (v - u)/t

=> a = -5/20 = -0.25 m/s²

Time varies from t = 0 s to t = 20 s and the equation is: v = 5 – 0.25t

So the graphs are:

For motorist A:

For motorist B: