Math

Question14. If a car accelerates at 9 m/s29 \mathrm{~m/s}^2, how long to reach 63 m/s63 \mathrm{~m/s}?
15. With 5 m/s25 \mathrm{~m/s}^2 acceleration, what speed after 10 s10 \mathrm{~s}?
16. In which direction are the horses moving?
17. Which horse is speeding up and which is slowing down?

Studdy Solution

STEP 1

Assumptions for problem141. The car's acceleration is constant at 9 \, \mathrm{m/s^} . The car starts from rest (initial velocity is 0m/s0 \, \mathrm{m/s})
3. We want to find the time it takes for the car to reach a speed of 63m/s63 \, \mathrm{m/s}

STEP 2

We use the formula for acceleration, which is change in velocity divided by time.
a=ΔvΔta = \frac{\Delta v}{\Delta t}

STEP 3

We rearrange the formula to solve for time.
Δt=Δva\Delta t = \frac{\Delta v}{a}

STEP 4

Now we substitute the given values into the formula.
Δt=63m/s9m/s2\Delta t = \frac{63 \, \mathrm{m/s}}{9 \, \mathrm{m/s^2}}

STEP 5

Calculate the time.
Δt=63m/s9m/s2=7s\Delta t = \frac{63 \, \mathrm{m/s}}{9 \, \mathrm{m/s^2}} =7 \, \mathrm{s}The car will take7 seconds to reach a speed of 63m/s63 \, \mathrm{m/s}.

STEP 6

Assumptions for problem151. The car's acceleration is constant at 5m/s25 \, \mathrm{m/s^2}
2. The car starts from rest (initial velocity is 0m/s0 \, \mathrm{m/s})
3. We want to find the speed of the car after 10s10 \, \mathrm{s}

STEP 7

We use the formula for acceleration, which is change in velocity divided by time.
a=ΔvΔta = \frac{\Delta v}{\Delta t}

STEP 8

We rearrange the formula to solve for change in velocity.
Δv=aΔt\Delta v = a \cdot \Delta t

STEP 9

Now we substitute the given values into the formula.
Δv=5m/s2s\Delta v =5 \, \mathrm{m/s^2} \cdot \, \mathrm{s}

STEP 10

Calculate the change in velocity, which is the speed of the car after 10s10 \, \mathrm{s}.
Δv=5m/s210s=50m/s\Delta v =5 \, \mathrm{m/s^2} \cdot10 \, \mathrm{s} =50 \, \mathrm{m/s}The car will be moving at a speed of 50m/s50 \, \mathrm{m/s} after 10s10 \, \mathrm{s}.

STEP 11

Problem16 and17 do not provide enough information to be solved. We need more details about the horses' movement to answer these questions.

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