Math

QuestionA cheetah runs at 30 m/s30 \mathrm{~m/s} and accelerates at 5 m/s25 \mathrm{~m/s^2} for 7 seconds. Find its final velocity.

Studdy Solution

STEP 1

Assumptions1. The initial velocity of the cheetah is 30 m/s30 \mathrm{~m/s} . The acceleration of the cheetah is 5 m/s5 \mathrm{~m/s}^{}
3. The time over which the cheetah accelerates is7 seconds4. We are asked to find the final velocity of the cheetah

STEP 2

We will use the formula for final velocity, which is given by the equationvf=vi+atv_f = v_i + a \cdot twhere- vfv_f is the final velocity- viv_i is the initial velocity- aa is the acceleration- tt is the time

STEP 3

Now, plug in the given values for the initial velocity, acceleration, and time to calculate the final velocity.
vf=30 m/s+5 m/s27 sv_f =30 \mathrm{~m/s} +5 \mathrm{~m/s}^{2} \cdot7 \mathrm{~s}

STEP 4

Perform the multiplication operation first (according to the order of operations, BIDMAS/BODMAS/PEDMAS).
vf=30 m/s+35 m/sv_f =30 \mathrm{~m/s} +35 \mathrm{~m/s}

STEP 5

Finally, add the two velocities to get the final velocity.
vf=30 m/s+35 m/s=65 m/sv_f =30 \mathrm{~m/s} +35 \mathrm{~m/s} =65 \mathrm{~m/s}The final velocity of the cheetah when it reaches the prey is 65 m/s65 \mathrm{~m/s}.

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