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Motion with constant acceleration - AS Maths

A car starts from rest at time t= 0. It accelerates uniformly until it's speed reaches Vm/s it travels at constant speed for 12 seconds and then decelerates uniformly coming to rest at t=26. The total distance travelled by the car is 840 metres. Find the value of V.

Hi, please could someone help me with this equation, no matter which way I look at it, I cannot find enough values to input into a SUVAT equation.

Thank you :smile:
Reply 1
Original post by PU_Student
A car starts from rest at time t= 0. It accelerates uniformly until it's speed reaches Vm/s it travels at constant speed for 12 seconds and then decelerates uniformly coming to rest at t=26. The total distance travelled by the car is 840 metres. Find the value of V.

Hi, please could someone help me with this equation, no matter which way I look at it, I cannot find enough values to input into a SUVAT equation.

Thank you :smile:


Just draw the velocity time graph and equate the area to the distance travelled.
You can draw a velocity time graph (which is usually the easiest way to approach this type of question), but if you want to understand how to use SUVAT for this, pop your working here and I'll see if I can help :smile:
Reply 3
velocitytimegraph.PNG
This is the velocity time graph I drew, from this I did:
840=(6+26)/2 * V (where V is the height/speed at that point)

840 = 16V
V=52.5

I would've thought this is the answer however it is 44.2 ms^-1.
I'm not sure if I have made a silly mistake or done the question completely incorrectly......
Reply 4
Original post by PU_Student
velocitytimegraph.PNG
This is the velocity time graph I drew, from this I did:
840=(6+26)/2 * V (where V is the height/speed at that point)

840 = 16V
V=52.5

I would've thought this is the answer however it is 44.2 ms^-1.
I'm not sure if I have made a silly mistake or done the question completely incorrectly......

The top of the trapezium is 12s long (duration). It gives the answer.
(edited 3 years ago)
Reply 5
Original post by PU_Student
velocitytimegraph.PNG
This is the velocity time graph I drew, from this I did:
840=(6+26)/2 * V (where V is the height/speed at that point)

840 = 16V
V=52.5

I would've thought this is the answer however it is 44.2 ms^-1.
I'm not sure if I have made a silly mistake or done the question completely incorrectly......

On your graph, you have only drawn the line being at constant speed for 6 seconds (12-18) but the question says the car was at constant speed for 12 seconds
Original post by PU_Student
velocitytimegraph.PNG
This is the velocity time graph I drew, from this I did:

EDIT - it is against the rules to post solutions
@Muttley79 - who are you talking to in your comment "it is against the rules to post solutions", as it appears the graphic you have quoted above your comment is by the OP?
Reply 8
Original post by aryeht
On your graph, you have only drawn the line being at constant speed for 6 seconds (12-18) but the question says the car was at constant speed for 12 seconds

Ah yes, I misread it. Thank you! :smile:

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