A car starts from rest and accelerates at a rate of 1 m/s^2 until it reaches a velocity of 7 m/s. It then travels at a constant velocity for the next 15 seconds. The driver then applies the brake, bringing the car to stop. The brakes provide an acceleration of -4 m/s^2.
a) what is the significance of the negative sign of the acceleration provided by the brakes?
b) determine the total amount of time that the car was in motion.
c) draw quantitatively correct graphs of the acceleration, velocity and position of the car as functions of time.
1562..3 N
a) The negative sign of the acceleration provided by the brakes indicates that the acceleration is in the opposite direction of the car's motion. In other words, the brakes are causing the car to slow down or decelerate. The negative sign is used to indicate a change in direction or a decrease in velocity.
b) To determine the total amount of time that the car was in motion, we need to analyze the different stages of its motion:
1. Acceleration phase: The car starts from rest and accelerates at a rate of 1 m/s^2 until it reaches a velocity of 7 m/s. To find the time taken during this acceleration phase, we can use the equation:
v = u + at
Here, u is the initial velocity (0 m/s), v is the final velocity (7 m/s), a is the acceleration (1 m/s^2), and t is the time taken. Rearranging the equation, we get:
t = (v - u) / a
= (7 - 0) / 1
= 7 seconds
2. Constant velocity phase: The car travels at a constant velocity for the next 15 seconds. Therefore, the time taken during this phase is 15 seconds.
3. Deceleration phase: The driver applies the brakes, causing the car to stop. The brakes provide an acceleration of -4 m/s^2. To find the time taken during this deceleration phase, we can use the same equation as in the acceleration phase:
t = (v - u) / a
= (0 - 7) / -4
= 1.75 seconds
Therefore, the total amount of time that the car was in motion is the sum of the times taken during each phase:
Total time = Acceleration time + Constant velocity time + Deceleration time
= 7 + 15 + 1.75
= 23.75 seconds
c) To draw quantitatively correct graphs of the acceleration, velocity, and position of the car as functions of time, we can use the following information:
- During the acceleration phase, the acceleration is constant at 1 m/s^2, and the velocity is increasing linearly from 0 m/s to 7 m/s. The position of the car also changes, accelerating from rest.
- During the constant velocity phase, the acceleration is 0 m/s^2, as the car is maintaining a constant velocity of 7 m/s. The velocity remains constant, but the position of the car continues to change at a constant rate.
- During the deceleration phase, the acceleration is constant at -4 m/s^2, and the velocity decreases linearly from 7 m/s to 0 m/s. The position of the car changes, decelerating until it comes to a stop.
By plotting these changes on appropriate graphs, we can accurately represent the motion of the car as functions of time.