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QuestionGiven the car's velocity at times 0−80-8 seconds: 10,15,20,25,30,30,30,15,010,15,20,25,30,30,30,15,0.
1. Direction from 0−40-4 seconds?
2. Direction from 4−64-6 seconds?
3. Direction from 6−86-8 seconds?
4. Acceleration from 4−64-6 seconds?

Studdy Solution

STEP 1

Assumptions1. The velocity of the car is given at different time intervals. . The direction of the car's movement is determined by the change in velocity.
3. A positive change in velocity indicates movement in the forward direction.
4. A negative change in velocity indicates movement in the backward direction.
5. No change in velocity indicates the car is moving in the same direction.
6. Acceleration is the rate of change of velocity with respect to time.

STEP 2

First, we need to determine the direction of the car's movement from 0−40-4 seconds. We can do this by comparing the velocity at 00 seconds and at 44 seconds.

STEP 3

The velocity at 00 seconds is 1010 and at $$ seconds is $30$. Since the velocity is increasing, the car is moving in the forward direction from $0-$ seconds.

STEP 4

Next, we need to determine the direction of the car's movement from 4−64-6 seconds. We can do this by comparing the velocity at 44 seconds and at 66 seconds.

STEP 5

The velocity at 44 seconds is 3030 and at $$ seconds is also $30$. Since the velocity is not changing, the car is moving in the same direction from $4-$ seconds.

STEP 6

Next, we need to determine the direction of the car's movement from 6−86-8 seconds. We can do this by comparing the velocity at 66 seconds and at 88 seconds.

STEP 7

The velocity at 66 seconds is 3030 and at $$ seconds is $0$. Since the velocity is decreasing, the car is moving in the backward direction from $6-$ seconds.

STEP 8

Finally, we need to calculate the acceleration of the car from 4−64-6 seconds. Acceleration is the rate of change of velocity with respect to time. It can be calculated using the formulaAcceleration=Final velocity−Initial velocityFinal time−Initial timeAcceleration = \frac{Final\, velocity - Initial\, velocity}{Final\, time - Initial\, time}

STEP 9

Plug in the values for the final velocity, initial velocity, final time, and initial time to calculate the acceleration.
Acceleration=30−306−4Acceleration = \frac{30 -30}{6 -4}

STEP 10

Calculate the acceleration.
Acceleration=02=0Acceleration = \frac{0}{2} =0The car's acceleration from 4−64-6 seconds is 00.
So, the car is moving in the forward direction from 0−40-4 seconds, in the same direction from 4−64-6 seconds, in the backward direction from 6−86-8 seconds, and the acceleration from 4−64-6 seconds is 00.

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