QuestionA car accelerates from rest to $60 \mathrm{~m/s}$ in 3 seconds. Find the displacement of the car. Identify variables.

Studdy Solution

STEP 1

Assumptions1. The initial velocity of the car is0 m/s (since it starts from rest) . The final velocity of the car is60 m/s3. The time taken to reach the final velocity is3 seconds4. The car is moving in a straight line (since it's a drag race)
5. The acceleration is constant during this time

STEP 2

We can use the formula for displacement under constant acceleration, which is given by $Displacement = Initial\, velocity \\times Time +0.5 \\times Acceleration \\times Time^2$

STEP 3

First, we need to find the acceleration of the car. We can do this by using the formula for acceleration, which is change in velocity divided by time.
$Acceleration = (Final\, velocity - Initial\, velocity) / Time$

STEP 4

Now, plug in the given values for the final velocity, initial velocity, and time to calculate the acceleration.
$Acceleration = (60\, m/s -0\, m/s) /3\, s$

STEP 5

Calculate the acceleration.
$Acceleration =60\, m/s /3\, s =20\, m/s^2$

STEP 6

Now that we have the acceleration, we can find the displacement of the car. Plug in the values for the initial velocity, acceleration, and time into the displacement formula.
$Displacement =0\, m/s \\times3\, s +0.5 \\times20\, m/s^2 \\times (3\, s)^2$

STEP 7

Calculate the displacement.
$Displacement =0 +0.5 \\times20\, m/s^2 \\times9\, s^2 =90\, m$ The displacement of the car is90 meters.

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