a 2100 kg car starts from rest and accelerates at a rate of 2.6 m/s for 4 sec. assume that the force acting to accelerate the car is acting in the same direction as its motion. how much work has the car done?
m=2100 kg w=fd
v1=0 f=ma
t=4 sec d=t+1/2at(squared)
a=2.6 m/s2
Well, if I were driving that car, I would probably be doing a lot more work trying to parallel park it. But let's focus on the question at hand.
To calculate the work done by the car, we need to find the force acting on the car and multiply it by the distance traveled. We already have the acceleration (a) and the time (t), so let's start there.
Using the formula d = 1/2at^2, we can calculate the distance traveled:
d = (1/2) * 2.6 m/s^2 * (4 sec)^2
d = 1/2 * 2.6 m/s^2 * 16 sec^2
d = 20.8 m
Now, we need to find the force acting on the car. We can use the formula F = ma:
F = 2100 kg * 2.6 m/s^2
F = 5460 N
Finally, we can calculate the work done (W = F * d):
W = 5460 N * 20.8 m
W = 113,568 J
So, the car has done 113,568 Joules of work. That's a lot more than I do in a day! Keep on truck...I mean, car-ing!
To find the work done by the car, we need to calculate the force acting on the car and the distance it travels during the acceleration.
First, let's calculate the force acting on the car using Newton's second law of motion: F = m * a
F = (2100 kg) * (2.6 m/s^2)
F = 5460 N
Next, let's calculate the distance the car travels during the acceleration using the equation: d = (1/2) * a * t^2
d = (1/2) * (2.6 m/s^2) * (4 sec)^2
d = 20.8 m
Finally, let's calculate the work done by the car using the equation: work = force * distance
work = (5460 N) * (20.8 m)
work = 113,568 J
Therefore, the car has done 113,568 Joules of work.
To calculate the work done by the car, we can use the formula:
Work (W) = Force (F) × Distance (d)
First, let's calculate the force acting on the car. The force can be determined using Newton's second law of motion:
Force (F) = mass (m) × acceleration (a)
F = 2100 kg × 2.6 m/s²
F = 5460 N
Next, we need to find the distance traveled by the car. We can calculate it using the equation of motion:
Distance (d) = initial velocity (v1) × time (t) + 1/2 × acceleration (a) × time (t)²
Since the car starts from rest, v1 = 0.
Distance (d) = 0 × 4 sec + 1/2 × 2.6 m/s² × (4 sec)²
Distance (d) = 0 + 1/2 × 2.6 m/s² × 16 sec²
Distance (d) = 1/2 × 2.6 m/s² × 16 sec²
Distance (d) = 20.8 meters
Finally, we can calculate the work done by the car:
Work (W) = Force (F) × Distance (d)
W = 5460 N × 20.8 meters
W = 113,568 joules
Therefore, the car has done 113,568 joules of work.