Question

A sprinter accelerates at 7.5 m/s from rest in 2.0 s, what distance did she go? (15 m)

Proof please

Answer 1

The sprinter traveled a distance of 7.5 m

Step-by-step explanation:

Motion With Constant Acceleration

It's a type of motion in which the rate of change of the velocity of an object is constant.

The equation that rules the change of velocities is:

`v_f=v_o+at\qquad\qquad [1]`

Where:

a = acceleration

vo = initial speed

vf = final speed

t = time

The distance traveled by the object is given by:

`\displaystyle x=v_o.t+(a.t^2)/(2)\qquad\qquad [2]`

Using the equation [1] we can solve for a:

`\displaystyle a=(v_f-v_o)/(t)`

The sprinter travels from rest (vo=0) to vf=7.5 m/s in t=2 s. Computing the acceleration:

`\displaystyle a=(7.5-0)/(2)`

`a=3.75\ m/s^2`

Now calculate the distance:

`\displaystyle x=0*2+(3.75*2^2)/(2)`

`\displaystyle x=7.5\ m`

The sprinter traveled a distance of 7.5 m