Question

5 you are riding a unicorn at 24 m/s and come to a uniform stop at a red light 28 m away. what was your acceleration? record your answer and fill in the bubbles on your answer document. be sure to use the correct place value. 6 a car starting from rest accelerates uniformly at 5.0 m/s² for 6.1 seconds. how far does the car move? record your answer and fill in the bubbles on your answer document. be sure to use the correct place value. 7 mrs. garcia is driving her car at a speed of 25 m/s when she sees an ambulance approaching behind her. to move out of the way and allow the ambulance to pass, she accelerates her car to a speed of 32 m/s in 3 seconds. what was mrs. garcias acceleration during those 3 seconds? record your answer and fill in the bubbles on your answer document. be sure to use the correct place value. 8 a driver is in a car traveling at a speed of 61.8 m/s. how long will it take for the car to decelerate uniformly to a stop in exactly 150 m? record your answer and fill in the bubbles on your answer document. be sure to use the correct place value.

Explanation:

5

Step1: Identify the known - values

Initial velocity $u = 24\ m/s$, final velocity $v = 0\ m/s$, distance $s = 28\ m$. Use the equation $v^{2}=u^{2}+2as$.

Step2: Rearrange the equation for acceleration

$a=\frac{v^{2}-u^{2}}{2s}$. Substitute $v = 0$, $u = 24\ m/s$, and $s = 28\ m$ into the formula.
$a=\frac{0 - 24^{2}}{2\times28}=\frac{- 576}{56}\approx - 10.3\ m/s^{2}$

Step1: Use the displacement - time formula for uniformly accelerated motion

The formula is $s=ut+\frac{1}{2}at^{2}$. Since the car starts from rest, $u = 0\ m/s$, $a = 5.0\ m/s^{2}$, and $t = 6.1\ s$.

Step2: Calculate the displacement

Substitute the values into the formula: $s=\frac{1}{2}\times5.0\times6.1^{2}=\frac{1}{2}\times5.0\times37.21 = 93.025\ m\approx93.0\ m$

Step1: Identify the known - values

Initial velocity $u = 25\ m/s$, final velocity $v = 32\ m/s$, time $t = 3\ s$. Use the acceleration formula $a=\frac{v - u}{t}$.

Step2: Calculate the acceleration

Substitute the values: $a=\frac{32 - 25}{3}=\frac{7}{3}\approx2.3\ m/s^{2}$

Answer:

$-10.3\ m/s^{2}$

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