Basic kinematics - calculating time

[v3ra]

A boy in a wagon starts from a rest position and then goes down a straight ramp, gaining
speed with uniform acceleration as he travels. In 6.00 s, he is traveling at 4.2 m/s.

a) What is his velocity at 10.0 s?

a = v2 – v1 / Δt
a = 4.2 m/s [down] – 0 / 6.0 s
a = 0.70 m/s^2 [down]

v2 = v1+a Δt
v2 = 0 + (0.70 m/s2) x 10.0 s
v2 = 7.0 m/s [down]

His velocity at 10.0 s is 7.0 m/s [down]


b) How long will it take him to reach a speed of 28.0 m/s?

This is where I am having trouble. I am unsure of the formula for calculating time. My book mentions Δt = v2 – v1 / Δt, but I believe this to be incorrect, so I tried Δt = v2 – v1 / a, but still could not get the answer they were looking for which is 40 seconds. Please advise.

 

[Doc Al]

so I tried Δt = v2 – v1 / a, but still could not get the answer they were looking for which is 40 seconds. Please advise.

That's the correct formula. (Just a rearrangement of the one you were using.) Why can't you get the answer? What did you plug in?

 

[sophiecentaur]

You are using the right equation but I wonder whether you are reading the question as they are hoping you should. I think they mean total time to reach 28m/s and not the extra time.

 

[v3ra]

That's the correct formula. (Just a rearrangement of the one you were using.) Why can't you get the answer? What did you plug in?

I am not sure what velocity to use, I was using 7.0 m/s for v2 and 0 for v1 and dividing it by 0.70 for acceleration.

 

[sophiecentaur]

For part b, they are dividing 28 (total change in speed from zero) by 0.7 (the accn. you calculated). I think you should read the question again!

 

[Doc Al]

I am not sure what velocity to use, I was using 7.0 m/s for v2 and 0 for v1 and dividing it by 0.70 for acceleration.

As sophiecentaur suggests, you need to reread the question. You were given the speed of 28.0 m/s for part b.

(7.0 m/s was the speed you found after 10 seconds.)