A 1.13 × 103 kg car accelerates uniformly from rest to 10.6 m/s in 3.22 s.
What is the work done on the car in this time interval?
Answer in units of J
W = F*d.
a = (V-Vo)/t
a = (10.6-0)/3.22 = 3.29 m/s^2.
F = m&a = 1130 * 3.29 = 3720 N.
d = 0.5a*t^2 = 0.5*3.29*(3.22^2)=17.1 m.
W = 3720 * 17.1 = 63,448 Joules.
To find the work done on the car, we can use the work-energy principle, which states that the work done on an object is equal to the change in its kinetic energy.
The formula for work done is:
Work = Force × Distance
However, in this case, we do not have the force and distance directly. Instead, we have the mass of the car and its final velocity, which means we need to find the acceleration and distance traveled first.
We know that acceleration is given by:
Acceleration = (Final Velocity - Initial Velocity) / Time
Plugging the given values into the formula, we get:
Acceleration = (10.6 m/s - 0 m/s) / 3.22 s
Acceleration = 10.6 m/s / 3.22 s
Acceleration ≈ 3.29 m/s²
Now, the distance traveled by the car can be calculated using the equation for uniform acceleration:
Distance = Initial Velocity × Time + (1/2) × Acceleration × Time²
Since the car starts from rest (initial velocity is 0), the equation simplifies to:
Distance = (1/2) × Acceleration × Time²
Distance = (1/2) × 3.29 m/s² × (3.22 s)²
Distance ≈ 5.58 m
Now we can calculate the work done on the car:
Work = Force × Distance
The force acting on the car is the product of its mass and acceleration:
Force = Mass × Acceleration
Force = 1.13 × 10³ kg × 3.29 m/s²
Force ≈ 3.72 × 10³ N
Finally, the work done is:
Work = Force × Distance
Work = 3.72 × 10³ N × 5.58 m
Work ≈ 2.08 × 10⁴ J
Therefore, the work done on the car in this time interval is approximately 2.08 × 10⁴ J.
To calculate the work done on the car, we can use the formula: Work (W) = Force (F) × Distance (d) × cosθ.
In this case, we don't have the force or distance directly, but we can find them using the formulae of physics.
First, we need to find the force (F) acting on the car. The force can be calculated using Newton's second law, which states that Force (F) = mass (m) × acceleration (a).
Given:
Mass (m) = 1.13 × 103 kg
Acceleration (a) = (final velocity - initial velocity) / time
= (10.6 m/s - 0 m/s) / 3.22 s
Now, we can calculate the acceleration:
a = (10.6 m/s - 0 m/s) / 3.22 s
= 3.29 m/s² (rounded to two decimal places)
Now, using Newton's second law, we can calculate the force:
F = m × a = 1.13 × 103 kg × 3.29 m/s²
Now that we have the force, we need to find the distance (d) over which the force is applied.
The distance can be calculated using the formula:
Distance (d) = (final velocity^2 - initial velocity^2) / (2 × acceleration)
= (10.6 m/s)^2 - (0 m/s)^2 / (2 × 3.29 m/s²)
Now, we can solve for the distance:
d = (10.6 m/s)^2 - (0 m/s)^2 / (2 × 3.29 m/s²)
Finally, we can calculate the work done on the car using the formula:
Work (W) = F × d × cosθ, where θ is the angle between the force and the direction of displacement. In this case, since the car is accelerating uniformly in a straight line, the angle θ is 0 degrees, and cosθ is 1.
Therefore, the work done on the car is:
W = F × d = (1.13 × 103 kg × 3.29 m/s²) × ((10.6 m/s)^2 - (0 m/s)^2 / (2 × 3.29 m/s²)) × 1
Simplifying this expression will give us the answer in units of joules (J).