13 A cyclist is travelling along a straight horizontal road. As she passes a bus

Question

13 A cyclist is travelling 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 constant speed of 3 mst for 20 seconds and then decelerates at a constant rate of 0.2 ms2 until coming to rest at the traffic light. (a) Calculate the distance between the bus stop and the traffic light. Calculate the time the cyclist takes to travel from the bus stop to the traffic light Calculate the average speed of the cyclist between the bus stop and the traffic light. (b) (c)

Explanation / Answer

Solution-  (a)
At constant speed she travelled a distance= 20 * 3 = 60 m
Now taking the situation when she was decelerating:
u = 3
a = -0.2
v = 0

Applying formula
v^2 - u^2 = 2ad

putting the values
0^2 - 3^2 = 2*(-0.2)*d
0 - 9 = -0.4d
-9 = -0.4d
d = (-9) / (-0.4)
d = 22.5
Hence the total distance:

60 + 22.5

= 82.5

(b)
Now when she was decelerating:
u = 3
a = -0.2
v = 0
v = u + at
0 = 3 - 0.2t
0.2t = 3
t = 3 / 0.2
t = 15
Hence

Total time=20 + 15

= 35 sec

(c) 82.5 / 35

=2.36 ms^-1

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