How Do You Calculate Displacement and Acceleration in a Kinematics Car Problem?

In summary, a car starts from rest heading due east and accelerates at 3.0m/s^2 for 5.0s. It then continues without further acceleration for 20.0s and finally brakes for 8.0s to come to rest. The car's velocity after the first 5.0 seconds is 15m/s and its acceleration over the last 8.0 seconds is -1.7m/s^2. The total displacement is 403.1m, with 37.5m in the first interval, 300m in the second interval, and 65.6m in the third interval.
  • #1
miamiheat5
14
0
A car starts from rest heading due east. It first accelerates at 3.0m/s^2 for 5.0s and then continues without further acceleration for 20.0s. It then brakes for 8.0s in coming to rest. (a) What is the car's velocity after the first 5.0 seconds? (b) What is the car's acceleration over the last 8.0s interval? (c) What is the total displacement?






The Attempt at a Solution



This is what i got: a) vf=vi+at
=0(3)(5)
vf=15m/s

b) vf=vi+at
0=15+a(8)
-15=a(8)
a=-1.7m/s^2

c) d1=37.5m
d2=300m
d3=65.6m
dtot=403.1m
 
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  • #2
miamiheat5 said:
This is what i got: a) vf=vi+at
=0(3)(5)
vf=15m/s

Correct.

b) vf=vi+at
0=15+a(8)
-15=a(8)
a=-1.7m/s^2
15/8 is not 1.7

c) d1=37.5m
d2=300m
d3=65.6m
dtot=403.1m

d3 would change based on the answer to b.
 
  • #3
ya it should be -1.9
 

1. What is kinematics in the context of car problems?

Kinematics is the study of the motion of objects without considering the causes of the motion, such as forces. In the context of car problems, it involves analyzing the position, velocity, and acceleration of a car as it moves.

2. How is kinematics used to solve car problems?

Kinematics is used to solve car problems by using mathematical equations and principles, such as displacement, velocity, and acceleration, to analyze the motion of the car. This can help determine factors such as the time it takes for the car to reach a certain distance or how much distance it will cover in a given time.

3. What is the difference between speed and velocity in kinematics?

Speed and velocity are often used interchangeably, but in kinematics, they have distinct meanings. Speed refers to the rate at which an object is moving, while velocity not only takes into account the speed but also the direction of motion.

4. How does acceleration affect the motion of a car in kinematics?

Acceleration is the rate at which an object's velocity changes. In the context of car problems, acceleration can affect the motion of a car by either increasing or decreasing its speed or changing its direction. It can also be used to calculate the force required to accelerate the car.

5. What is the significance of kinematic equations in solving car problems?

Kinematic equations, such as the equations for displacement, velocity, and acceleration, are essential tools in solving car problems. These equations provide a mathematical framework for analyzing the motion of a car and can be used to predict future positions and speeds of the car. They also allow us to determine the factors that affect the car's motion, such as time, distance, and acceleration.

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