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A car of mass 300kg starts from rest and travels upwards along a straight road of 450m inclined at an angle of 5 degree to the horizontal and the speed of the car is 28m/s at the top of the slope. Determine its acceleration, the time taken to travel, the length of the slope, gain in kinetic energy and gain in gravitational potential energy

User Shpand
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2 Answers

3 votes

Final answer:

The acceleration of the car is 0.873 m/s^2, the time taken to travel is 32.09 s, the length of the slope is 450 m, the gain in kinetic energy is 117,600 J, and the gain in gravitational potential energy is approximately 40.41 m.

Step-by-step explanation:

To determine the acceleration of the car, we can use the equation:

a = (v^2 - u^2)/(2s)

Where:

  • a is the acceleration
  • v is the final velocity
  • u is the initial velocity
  • s is the distance traveled

Plugging in the given values, we have:

a = (28^2 - 0^2)/(2 * 450) = 0.873 m/s^2

To calculate the time taken to travel, we can use the equation:

t = (v - u)/a

Plugging in the values, we have:

t = (28 - 0)/0.873 = 32.09 s

The length of the slope is given as 450 m.

The gain in kinetic energy can be calculated using the equation:

ΔKE = 0.5 * m * (v^2 - u^2)

Plugging in the values, we have:

ΔKE = 0.5 * 300 * (28^2 - 0^2) = 117,600 J

The gain in gravitational potential energy can be calculated using the equation:

ΔPE = m * g * h

Where:

  • ΔPE is the gain in potential energy
  • m is the mass
  • g is the acceleration due to gravity (approximately 9.8 m/s^2)
  • h is the vertical height

Since we know the final speed at the top of the slope, the car has gained all its potential energy. Therefore, we can equate these two expressions:

ΔPE = ΔKE

m * g * h = 0.5 * m * (v^2 - u^2)

Cancelling out the mass, we have:

g * h = 0.5 * (v^2 - u^2)

Plugging in the values, we have:

9.8 * h = 0.5 * (28^2 - 0^2)

Simplifying, we get:

h ≈ 40.41 m

User MadNik
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4.9k points
1 vote

Answer:

Look at the picture.

Step-by-step explanation:

I solved all of questions except the length of the slope because I don't know about it.

A car of mass 300kg starts from rest and travels upwards along a straight road of-example-1
User Cvarsendan
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4.5k points