If an object with uniform acceleration (or deceleration) has a speed of $3 \frac{m}{s}$ $3 m/s$ at $t = 0$ $t=0$ and moves a total of 25 m by $t = 8$ $t=8$ , what was the object's rate of acceleration?

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If an object with uniform acceleration (or deceleration) has a speed of $3 \frac{m}{s}$ $3 m/s$ at $t = 0$ $t=0$ and moves a total of 25 m by $t = 8$ $t=8$ , what was the object's rate of acceleration?

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Answer 1 · 2016-04-16T01:23:50

$0.03 \frac{m}{s^{2}}$ $0.03m/s^2$

Explanation:

Recall the following kinematic formula of motion:

$∣ ∣ ∣ ∣ ∣ ¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯ \frac{a}{a} Δ d = v_{i} Δ t + \frac{1}{2} a Δ t^{2} \frac{a}{a} ∣ ∣ ∣ - --------------------- -$ $color(blue)(|bar(ul(color(white)(a/a)Deltad=v_iDeltat+1/2aDeltat^2color(white)(a/a)|)))$

where:
$Δ d =$ $Deltad=$ change in distance
$v_{i} =$ $v_i=$ initial velocity
$Δ t =$ $Deltat=$ change in time
$a =$ $a=$ acceleration

Start by listing out the given and required values.

$v_{i} = 3 \frac{m}{s}$ $v_i=3m/s$

$Δ d = 25 m$ $Deltad=25m$

$t = 8 s$ $t=8s$

$a = ?$ $a=?$

Notice how the only variable to solve for is $a$ $a$ .

Thus, rearrange the formula for $a$ $a$ and plug in your known values into the formula to find the acceleration of the object.

$Δ d = v_{i} Δ t + \frac{1}{2} a Δ t^{2}$ $Deltad=v_iDeltat+1/2aDeltat^2$

$= \frac{1}{2} a Δ t^{2} = Δ d - v_{i} Δ t$ $=1/2aDeltat^2=Deltad-v_iDeltat$

$= \frac{2 (Δ d - v_{i} Δ t)}{Δ t^{2}}$ $=(2(Deltad-v_iDeltat))/(Deltat^2)$

$= \frac{2 (25 m - (3 \frac{m}{s} (8 s)))}{{(8 s)}^{2}}$ $=(2(25m-(3m/s(8s))))/(8s)^2$

$= 0.03125 \frac{m}{s^{2}}$ $=0.03125m/s^2$

$\approx ∣ ∣ ∣ ∣ ¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯ \frac{a}{a} 0.03 \frac{m}{s^{2}} \frac{a}{a} ∣ ∣ ∣ - --------- -$ $~~color(green)(|bar(ul(color(white)(a/a)0.03m/s^2color(white)(a/a)|)))$

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If an object with uniform acceleration (or deceleration) has a speed of $3 \frac{m}{s}$ $3 m/s$ at $t = 0$ $t=0$ and moves a total of 25 m by $t = 8$ $t=8$ , what was the object's rate of acceleration?

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If an object with uniform acceleration (or deceleration) has a speed of $3 \frac{m}{s}$ $3 m/s$ at $t = 0$ $t=0$ and moves a total of 25 m by $t = 8$ $t=8$ , what was the object's rate of acceleration?