Question

A motorcyclist starts from rest at a point S on a straight race track. He moves with constant acceleration for 15 s, reaching a velocity of 30ms⁻¹. He then travels at a constant velocity of 30ms⁻¹ for T seconds. Finally he decelerates at a constant rate coming to rest at a point F, 25s after he begins to decelerate:

a Sketch a velocity-time graph to illustrate the motion.Given that the distance between S and Fis 2.4 km :
b calculate the time the motorcyclist takes to travel from S to F. (3 marks)

Answer 1

The motorcyclist takes a total of 15 + T seconds to travel from S to F, and T can be determined by solving an equation. The time is found to be 75 seconds.

Step-by-step explanation:

The velocity-time graph for the motion of the motorcyclist can be divided into three segments: acceleration, constant velocity, and deceleration.

In the acceleration segment, the velocity starts from rest and increases with a constant acceleration for 15 seconds until it reaches 30 m/s.

In the constant velocity segment, the velocity remains constant at 30 m/s for T seconds.

In the deceleration segment, the velocity decreases with a constant deceleration until it comes to rest 25 seconds after the deceleration begins.

To calculate the time the motorcyclist takes to travel from S to F, we need to add the durations of the acceleration and constant velocity segments. Therefore, the total time is 15 + T seconds.

Given that the distance between S and F is 2.4 km, or 2400 m, we can use the equation: distance = average velocity x time. Since the average velocity is constant during the constant velocity segment, it is equal to 30 m/s. So, 2400 = 30 x (15 + T). Solving for T, we get T = 75 seconds.