# Calculate acceleration and time given initial speed, final speed, and travelling distance?

14,182

For constant acceleration, you have two equations that you need to solve for time $$t$$ and acceleration $$a$$.

$$x=\frac12at^2$$ $$v=at$$

It is up to you from here.

$$402\ \mathrm m=\frac12at^2$$ $$\left(190\ \mathrm{\frac{km}h}\right)\left(\frac{1000\ \mathrm{\frac m{km}}}{3600\ \mathrm{\frac sh}}\right)=\left(52.777\ \mathrm{\frac ms}\right)at$$

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### pilau

Updated on June 16, 2022

• A motorcycle is known to accelerate from rest to 190km/h in 402m.

Considering the rate of acceleration is constant, how should I go about calculating the acceleration rate and the time it took the bike to complete the distance?

• aries0152 over 9 years
Try v=u+at for acceleration.
• pilau over 9 years
But I don't know how long it took the bike to cover the stretch. I only know Vi (0), Vf (190km/h), and d (402m).
• Alan Rominger over 9 years
You are correct that you need more than just that equation. The other kinematic equation you might want to use is $x=1/2 a t^2$, which uses the fact that you started from rest and had a constant acceleration. I'd advise reading a basic kinematics tutorial online.
• pilau over 9 years