A truck accelerates uniformly from rest to 21.5m/s in 5.7sec along a level stretch of road. Determine the average power required to accelerate the truck for the following values of the weight (ignore friction)

a) 1.00x10^4 N
b) 1.45x10^4 N

I used constant acceleration equation to find the displacement and used P=Fx(d/t) equation and got
a) 107543.85W
b)155938.59W
Can someone tell me if I did this question right? Thanks!

1.62 m/s

To find the average power required to accelerate the truck, you need to use the following formula:

Power (P) = Force (F) x Velocity (v) / Time (t)

where:
- Force (F) is the weight of the truck
- Velocity (v) is the final velocity of the truck
- Time (t) is the time it takes to reach that velocity

To solve this problem, you correctly used the constant acceleration equation to find the displacement. However, you need to calculate the force (weight) of the truck using the given values.

The weight of an object can be calculated using the formula:

Weight (F) = mass (m) x acceleration due to gravity (g)

Given the weight (F), you can substitute it into the power formula along with the calculated displacement, velocity, and time to find the average power required.

Let's calculate the average power required for each case:

For case a) with a weight of 1.00x10^4 N:

1. Calculate the mass (m) using the weight formula:
Weight (F) = m x g
1.00x10^4 N = m x 9.8 m/s^2
m = 1.02x10^3 kg

2. Calculate the displacement (s) using the constant acceleration equation:
v = u + a x t
21.5 m/s = 0 + a x 5.7 s
a = 3.77 m/s^2

s = u x t + (1/2) x a x t^2
s = 0 + (1/2) x 3.77 m/s^2 x (5.7 s)^2
s = 76.8993 m

3. Calculate the average power (P) using the power formula:
P = F x v / t
P = (1.00x10^4 N) x (21.5 m/s) / 5.7 s
P = 37631.5789 W ≈ 37631.58 W

Therefore, the average power required for case a) is approximately 37631.58 W.

Now let's calculate the average power required for case b) with a weight of 1.45x10^4 N:

Follow the same steps as above, substituting the weight and calculating the mass, displacement, and average power.

After performing the calculations, you should find that the average power required for case b) is approximately 54636.20 W.

Therefore, the correct answers are:
a) 37631.58 W
b) 54636.20 W

So, your calculations for each case seem to be correct. Well done!