If an object with uniform acceleration (or deceleration) has a speed of $2 \frac{m}{s}$ $2 m/s$ at $t = 0$ $t=0$ and moves a total of 20 m by $t = 4$ $t=4$ , what was the object's rate of acceleration?

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If an object with uniform acceleration (or deceleration) has a speed of $2 \frac{m}{s}$ $2 m/s$ at $t = 0$ $t=0$ and moves a total of 20 m by $t = 4$ $t=4$ , what was the object's rate of acceleration?

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Answer 1 · 2016-07-02T20:28:05

$a = 1.5 \frac{m}{s^{2}}$ $a=1.5m/s^2$

Explanation:

This is interesting. The question gives us an ambiguity as to whether the acceleration is positive or negative. We can solve this using the first kinematic equation.

We'll establish the variables first. $u = 2 \frac{m}{s}$ $u=2m/s$ , $t = 4$ $t=4$ , $x = 20 m$ $x=20m$

We'll use the first kinematic equation now.
$x = u t + \frac{1}{2} a t^{2}$ $x=ut+1/2at^2$
So, that ends us with $20 = 2 \cdot 4 + \frac{1}{2} \cdot a \cdot 16$ $20=2*4+1/2*a*16$
Rearranging, $20 - 8 = 8 a \Rightarrow 12 = 8 a \Rightarrow 1.5 \frac{m}{s^{2}} = a$ $20-8=8a\implies12=8a\implies1.5m/s^2=a$

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If an object with uniform acceleration (or deceleration) has a speed of $2 \frac{m}{s}$ $2 m/s$ at $t = 0$ $t=0$ and moves a total of 20 m by $t = 4$ $t=4$ , what was the object's rate of acceleration?

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If an object with uniform acceleration (or deceleration) has a speed of $2 \frac{m}{s}$ $2 m/s$ at $t = 0$ $t=0$ and moves a total of 20 m by $t = 4$ $t=4$ , what was the object's rate of acceleration?