Question

Consider a mass initially moving at 7.50 m/s. How does it take to move 3.5 km (Be sure to convert to meters) if it accelerates at .550 m/s^2.?

Please show your work.

Answer 1

The mass is moving by uniformly accelerated motion, with initial velocity
`v_i=7.50 m/s` and acceleration
`a=0.55 m/s^2`. Its position at time t is given by the following law:

`x(t)=v_i t + (1)/(2)at^2`
where we take the initial position
`x_i=0` since we are only interested in the distance traveled by the mass.

If we put
`x(t)=d=3.5 km=3500 m` into the equation, the corresponding time t is the time it takes for the mass to travel this distance:

`(1)/(2)at^2+v_it-d=0`

`4.9t^2+7.5t-3500 =0`
And the two solutions for the equation are:

`t=-25.5 s` --> negative, we can discard it

`t=24.0 s` --> this is the solution to our problem