QuestionA car accelerates from $50 \mathrm{mph}$ to $80 \mathrm{mph}$ in 5 seconds. Find the car's acceleration.

Studdy Solution

STEP 1

Assumptions1. The initial speed of the car is50 mph. The final speed of the car is80 mph3. The time taken for this change in speed is5 seconds4. We need to convert the speeds from mph to m/s to calculate acceleration in standard units

STEP 2

First, we need to convert the initial and final speeds from miles per hour (mph) to meters per second (m/s). We can do this by multiplying the speed in mph by a conversion factor of0.44704.
$Speed_{m/s} = Speed_{mph} \\times0.44704$

STEP 3

Now, plug in the given values for the initial and final speeds to calculate these in m/s.
$Initial\, speed_{m/s} =50\, mph \\times0.44704$ $Final\, speed_{m/s} =80\, mph \\times0.44704$

STEP 4

Calculate the initial and final speeds in m/s.
$Initial\, speed_{m/s} =50\, mph \\times0.44704 =22.352\, m/s$ $Final\, speed_{m/s} =80\, mph \\times0.44704 =35.7632\, m/s$

STEP 5

Now that we have the initial and final speeds in m/s, we can calculate the acceleration. Acceleration is the change in velocity divided by the time taken for this change.
$Acceleration = (Final\, speed - Initial\, speed) / Time$

STEP 6

Plug in the values for the final speed, initial speed, and time to calculate the acceleration.
$Acceleration = (35.7632\, m/s -22.352\, m/s) /5\, s$

STEP 7

Calculate the acceleration.
$Acceleration = (35.7632\, m/s -22.352\, m/s) /5\, s =2.68224\, m/s^2$ The acceleration of the car is $2.68224 \, m/s^2$ .

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