Thread: SUVAT help please (mechanics)

I have this question, but cannot rearrange any of the SUVAT equations to get the answer:

A set of traffic lights covers road repairs on a road. The traffic lights are 80m apart. Assume a car accelerates at 2ms^2 from rest until reaching a speed of 10ms^1 and then travels at a constant speed. What is the least time taken for a car starting from rest at the first set of lights to reach the next set?

****************

S= 80m
U= 0ms^1
V= 10ms^1
A= 2ms^2
T= ?

The answer is 10.5 seconds, the closest I have got is 8.9 seconds by rearranging s= ut + 1/2at^2 into the form of the quadratic formula. Otherwise I have not come anywhere close to the answer, and I dont know how, as Im certain Ive rearranged the suvat equations properly.

Please help

thanks

Originally Posted by fishkeeper

I have this question, but cannot rearrange any of the SUVAT equations to get the answer:

A set of traffic lights covers road repairs on a road. The traffic lights are 80m apart. Assume a car accelerates at 2ms^2 from rest until reaching a speed of 10ms^1 and then travels at a constant speed. What is the least time taken for a car starting from rest at the first set of lights to reach the next set?

****************

S= 80m
U= 0ms^1
V= 10ms^1
A= 2ms^2
T= ?

The answer is 10.5 seconds, the closest I have got is 8.9 seconds by rearranging s= ut + 1/2at^2 into the form of the quadratic formula. Otherwise I have not come anywhere close to the answer, and I dont know how, as Im certain Ive rearranged the suvat equations properly.

Please help

thanks

to use the kinematics equations, you must break this problem into two parts because acceleration is not constant over the entire trip.

start at 2 m/s^2 from v = 0 until v = 10 m/s is 5 seconds

for that 5 seconds, s = (1/2)at^2 = 25 m

you still have 80-25 = 55 m left to travel at a constant 10 m/s

that will take 55/10 = 5.5 more seconds

5 s + 5.5 s = 10.5 s