An antelope moving with constant acceleration covers the distance between

An antelope moving with constant acceleration covers the distance between two points 70.0 m apart in 6.00 s. Its speed as it passes the second point is 15.0 m/s. What are (a) its speed at the first point and (b) its acceleration?

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limacarp4

a) Since that is a motion with a constant acceleration, we can use the following two equations
${v}_{x}={v}_{x,0}+{a}_{x}t$
$x-{x}_{o}={v}_{x,o}t+\frac{1}{2}{a}_{x}{t}^{2}$
where () is the speed at the second point, $\left(x-{x}_{o}=70\right)$ is the traveled distance and t=6 s. Substitutte for ${v}_{x},{a}_{x}$ and t into the two equations to get the following
$15\frac{m}{s}={v}_{x,o}+\left(6s\right){a}_{x}$
rearrange the equation to isolate ${a}_{x}$

Substitute for ${a}_{x}$ from equation (1) into equation (2)

rearrange the equation and solve to find ${v}_{x,o}$

b) The acceleration can be determined by substituting the value of ${v}_{x,o}$ into equation