Math

QuestionA car accelerates from rest to 60 m/s60 \mathrm{~m/s} in 3 seconds. Find the acceleration rate. Given: 60 m/s60 \mathrm{~m/s}, 33 s, 0 m/s0 \mathrm{~m/s}.

Studdy Solution

STEP 1

Assumptions1. The initial velocity of the car is 0 m/s0 \mathrm{~m/s} . The final velocity of the car is 60 m/s60 \mathrm{~m/s}
3. The time taken to reach the final velocity from rest is 33 seconds4. The acceleration is constant

STEP 2

We can use the formula for acceleration, which is the change in velocity divided by the time taken for that change.
a=vfvita = \frac{{v_f - v_i}}{t}where- aa is the acceleration- vfv_f is the final velocity- viv_i is the initial velocity- tt is the time

STEP 3

Now, plug in the given values for the final velocity, initial velocity, and time into the acceleration formula.
a=60 m/s0 m/s3 sa = \frac{{60 \mathrm{~m/s} -0 \mathrm{~m/s}}}{3 \mathrm{~s}}

STEP 4

implify the numerator in the fraction.
a=60 m/s3 sa = \frac{{60 \mathrm{~m/s}}}{3 \mathrm{~s}}

STEP 5

Calculate the acceleration.
a=60 m/s3 s=20 m/s2a = \frac{{60 \mathrm{~m/s}}}{3 \mathrm{~s}} =20 \mathrm{~m/s^2}The acceleration rate of the car is 20 m/s220 \mathrm{~m/s^2}.

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