What is the Acceleration of a Vehicle at Different RPMs?

In summary, to find the acceleration of a vehicle at 3k rpm and 5k rpm, we can use the equations kW = HP*0.7457, Nm (torque) = (kW*9550)/RPM, and Total Newtons =Nm*(Gear ratio) / Tire Radius in meters. Neglecting any losses, we can calculate the acceleration to be approximately 1.23m/s2.
  • #1
Triple88a
18
0

Homework Statement


Find the Acceleration of a vehicle at 3k rpm and 5k rpm.
At 3k the engine produces 65hp. At 5k it produces 155hp.
Car weight is 1000kg. The wheels are 50cm in diameter. The engine is connected to the wheel via 2:1 ratio transmission. Neglect any losses.

Homework Equations


kW = HP*0.7457 Nm (torque) = (kW*9550)/RPM
Total Newtons =Nm*(Gear ratio) / Tire Radius in meters
Acceleration: MA = F ... Total Newtons / Car weight.

The Attempt at a Solution


kW = 65*.7457 = 48kW 48*9550/3000 = 154Nm (torque at 3k rpm)
154Nm*2/.25m = 1232N
MA= F... F/M = A 1232N / 1000 = 1.232MS^2 but for some reason that doesn't seem right. Others are getting different results so I'm not sure whos wrong.

The 5k is the same formulas so no point of posting that as well.

Thanks for reading.
 
Last edited:
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  • #2
Looks like you forgot to account for the transmission ratio.
 
  • #3
billy_joule said:
Looks like you forgot to account for the transmission ratio.
The Transmission ratio is the 2nd number.

154Nm*2/.25m = 1232N 154Nm * 2 since 1:2 tranny doubles the torque / the leverage of the tire. No?
 
  • #4
Triple88a said:
The Transmission ratio is the 2nd number.

154Nm*2/.25m = 1232N 154Nm * 2 since 1:2 tranny doubles the torque / the leverage of the tire. No?

Ah, I missed that. In that case I'd agree with your answer.

Triple88a said:
The engine is connected to the wheel via 1:2 ratio transmission.
I guess this could be interpreted (incorrectly IMO) as:
engine:wheel = 1:2
Which results in a ridiculous road speed of 942 km/h @ 5000rpm
 
  • #5
For what it's worth, I get the same answer by a different route.
3000rpm=50rps, or 25rps at the wheels.
25π0.5=39m/s (about 140kph)
F=P/v=48kW/39m/s=approx 1200N.
 
  • #6
Is the Acceleration in M/S2 correct?
 
  • #7
Triple88a said:
Is the Acceleration in M/S2 correct?
making my calculation in post #5 a little more accurate, 1230N. 1230N/1000kg=1.23m/s2.
 
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1. What is acceleration?

Acceleration is the rate of change of an object's velocity over time. This means that it is how quickly an object's speed is increasing or decreasing.

2. How is acceleration measured?

Acceleration is typically measured in meters per second squared (m/s²). This unit represents how much an object's speed changes in one second.

3. What factors affect the acceleration of a vehicle?

The acceleration of a vehicle is affected by the engine's power, the mass of the vehicle, and the friction between the tires and the road. Other factors such as air resistance and incline of the road can also impact acceleration.

4. How does acceleration affect the motion of a vehicle?

Acceleration can either increase or decrease the speed of a vehicle. When a vehicle accelerates, it gains speed in the direction of motion. When it decelerates, it loses speed in the opposite direction of motion.

5. What is the difference between acceleration and velocity?

Acceleration and velocity are related, but they are not the same. Velocity is the speed and direction of an object's motion, while acceleration is the rate of change of velocity. In other words, velocity tells us how fast and in what direction an object is moving, while acceleration tells us how quickly that motion is changing.

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