# The Power Needed to Accelerate

## Homework Statement

Hi, guys. I'm in a bit of a quandary. I'm trying to calculate the power a motor should have in order to move a mass a certain distance. My calculation keeps telling me that the horsepower output is much lower than my reference scenario. Here's the situation. I'm trying to figure out how to accelerate a 1633 kg object a distance of 2 m in 1 sec.
m = 1633 kg
d = 2 meters
t = 1 sec

F=ma
P=F(d/t)

## The Attempt at a Solution

Acceleration is thus 2 m/(s^2). According to F=ma, F = 3266 Newtons. Plugging this into P=F(d/t), where d=2m, t=1 sec, Power needed = 6532 Watts or approx 8.8 hp. The problem is in a similar situation, a 215 hp propulsion system is needed to provide the thrust to accelerate and sustain a mass of 95 kg above ground. Where is this discrepancy coming from? My calculations clearly do not correlate with the already established real world scenario. Can I get some direction in this issue?

## Answers and Replies

PhanthomJay
Science Advisor
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Use the kinematic motion equations
to solve for acceleration. Your formula for power yields average power, not max power at the 2 meter mark

• Zachary Kempler
CWatters
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+1. The required acceleration is not 2m/s^2.

If the acceleration is constant the power isn't constant and the max power will occur at max velocity.

haruspex
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2020 Award
trying to calculate the power a motor should have
Turning around the preceding responses, your situation is constant power, so not constant acceleration.
The SUVAT equations will therefore not apply. You need to work instead with the more general differential forms.
Work done in time t ##=Pt=\frac 12 mv^2##. Can you solve to find position as a function of time?

CWatters
Science Advisor
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Gold Member
Perhaps we need the OP to clarify...

Does the motor generate a constant power? Does it have a power vs velocity or rpm curve?