## Linear motion with variable forces

1. The problem statement, all variables and given/known data
A racing car of mass 20000kg accelerates with a driving force of 480(t-10)^2 newtons until it reaches its maximum speed after 10 seconds. Find its maximum speed, and the distance it travels in reaching this speed.

3. The attempt at a solution
Again, I can't seem to get the distance travelled after the second integration.
m=2000kg
F=480(t-10)^2
a=F/m
= 6(t-10)^2/25
v=∫a dt
=[6(t-10)^3/3]/25 + k
Since t=0, v=0 and therefore v=[6(t-10)^3/3]/25
Vmax is found out to be 80m/s

But integration of v did not give me the answer stated, which is 600m. I got 200m instead.

Please include detailed explanations along with the solution. Thanks! :D
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 Quote by jiayingsim123 1. The problem statement, all variables and given/known data A racing car of mass 20000kg accelerates with a driving force of 480(t-10)^2 newtons until it reaches its maximum speed after 10 seconds. Find its maximum speed, and the distance it travels in reaching this speed. 3. The attempt at a solution Again, I can't seem to get the distance travelled after the second integration. m=2000kg F=480(t-10)^2 a=F/m = 6(t-10)^2/25 v=∫a dt =[6(t-10)^3/3]/25 + k Since t=0, v=0 and therefore v=[6(t-10)^3/3]/25 Vmax is found out to be 80m/s But integration of v did not give me the answer stated, which is 600m. I got 200m instead. Please include detailed explanations along with the solution. Thanks! :D
What is the mass?
 Sorry the mass is 2000kg. :)

## Linear motion with variable forces

For the velocity you can also use F=dp/dt
$\int_0^t \! f(t) \, \mathrm{d} t. =\int_0^v \! f(mv) \, \mathrm{d} v.$

Just find v from acceleration by integral
Then find d from v by integral too.

Recognitions:
Homework Help
 Quote by jiayingsim123 a=F/m = 6(t-10)^2/25 v=∫a dt =[6(t-10)^3/3]/25 + k Since t=0, v=0 and therefore v=[6(t-10)^3/3]/25
Your initial velocity is -80 instead of zero. Choose other value for k.

ehild

 Tags calculus, integration, linear motion