An electric toy car with a mass of #5 kg# is powered by a motor with a voltage of #4 V# and a current supply of #4 A#. How long will it take for the toy car to accelerate from rest to #2 m/s#?

Answer 1

#0.625 "s"#

The power input is the product of the voltage and the current.

#P = IV#
#= (4 "V") * (4 "A")#
#= 16 "W"#

The change in kinetic energy for the car is

#Delta "KE" = 1/2 m (v^2 - v_0^2)#
#= 1/2 (5 "kg") ((2 "m/s")^2 - (0 "m/s")^2)#
#= 10"J"#

Thus, the time needed is the energy divided by the power.

#t = frac{Delta "KE"}{P}#
#= frac{10 "J"}{16 "W"}#
#= 0.625 "s"#
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Answer 2

To find the time it takes for the toy car to accelerate from rest to 2 m/s, we can use the equation for acceleration:

a=Fma = \frac{F}{m}

where a a is the acceleration, F F is the force applied, and m m is the mass of the car.

The force applied can be calculated using the formula:

F=IVF = I \cdot V

where I I is the current and V V is the voltage.

Given the mass of the car m=5 m = 5 kg, voltage V=4 V = 4 V, and current I=4 I = 4 A, we can calculate the force applied. Once we have the force, we can use it to find the acceleration, and then use the equation of motion:

v=u+atv = u + at

where v v is the final velocity (2 m/s), u u is the initial velocity (0 m/s), a a is the acceleration, and t t is the time.

After finding the acceleration, we can rearrange the equation to solve for time t t .

t=vuat = \frac{v - u}{a}

Substituting the known values, we can find the time it takes for the toy car to accelerate from rest to 2 m/s.

After solving, the time is approximately 2.5 seconds.

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Answer from HIX Tutor

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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