Distance travelled with constant velocity or constant acceleration

[Physics1854]

Homework Statement

A cyclist is traveling along a straight horizontal road. as she passes a bus stop she sees a red traffic light ahead of her. She continues to travel with a constand speed of 3 ms^-1 for 20 seconds and then decelerates at a constant rate of 0.2ns^-2 until coming to rest at the traffic light

Homework Equations

a) calculate the distance between the bus stop and the traffic light

b) calculate the time the cyclist takes to travel from the bus stop to the traffic light

c) calculate the average speed of the cyclist between the bus stop and the traffic light

The Attempt at a Solution

 

[rl.bhat]

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[tomcue]

a) To calculate the distance, we can use the formula d = vt, where d is the distance, v is the velocity, and t is the time. In this case, the distance would be 3 ms^-1 * 20 s = 60 m. This is the distance the cyclist travels at a constant speed before decelerating.

b) To calculate the time, we can use the formula t = (vf - vi)/a, where t is the time, vf is the final velocity, vi is the initial velocity, and a is the acceleration. In this case, the initial velocity is 3 ms^-1, the final velocity is 0 ms^-1 (since the cyclist comes to a stop), and the acceleration is -0.2 ms^-2. Plugging in these values, we get t = (0 - 3)/(-0.2) = 15 s. This is the time it takes for the cyclist to decelerate from a constant speed of 3 ms^-1 to a stop.

c) To calculate the average speed, we can use the formula v = d/t, where v is the average speed, d is the distance, and t is the time. In this case, the average speed would be 60 m / 15 s = 4 ms^-1. This is the average speed of the cyclist between the bus stop and the traffic light.