Math Snap

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 $0-4$ seconds. We can do this by comparing the velocity at $0$ seconds and at $4$ seconds.

STEP 3

The velocity at $0$ seconds is $10$ 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 $4-6$ seconds. We can do this by comparing the velocity at $4$ seconds and at $6$ seconds.

STEP 5

The velocity at $4$ seconds is $30$ 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 $6-8$ seconds. We can do this by comparing the velocity at $6$ seconds and at $8$ seconds.

STEP 7

The velocity at $6$ seconds is $30$ 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 $4-6$ seconds. Acceleration is the rate of change of velocity with respect to time. It can be calculated using the formula$$Acceleration = \frac{Final\, velocity - Initial\, velocity}{Final\, time - Initial\, time}$$

STEP 9

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

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