An electric toy car with a mass of #3 kg# is powered by a motor with a voltage of #7 V# and a current supply of #1 A#. How long will it take for the toy car to accelerate from rest to #5/3 m/s#?
Electrical power is
and mechanical power is
so
Rearrange the equation for time, which we want to find:
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To calculate the time it takes for the toy car to accelerate from rest to 5/3 m/s, you can use the equation:
[ t = \frac{m \cdot v}{F} ]
where (t) is the time, (m) is the mass of the car, (v) is the final velocity, and (F) is the force acting on the car.
First, calculate the force acting on the car using the equation:
[ F = I \cdot V ]
where (I) is the current and (V) is the voltage.
Then, use the force to find the time:
[ t = \frac{m \cdot v}{F} ]
Substitute the given values into the equations and solve for (t).
[ F = 1 , \text{A} \cdot 7 , \text{V} = 7 , \text{N} ]
[ t = \frac{3 , \text{kg} \cdot \frac{5}{3} , \text{m/s}}{7 , \text{N}} ]
[ t = \frac{5}{7} , \text{s} ]
So, it will take approximately (0.714) seconds for the toy car to accelerate from rest to (5/3 , \text{m/s}).
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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