A cheetah is hiding in the grass. IT spots a zebra and bursts to a top speed of 20 m/s in a space of 48 meters.

Question

A cheetah is hiding in the grass. IT spots a zebra and bursts to a top speed of 20 m/s in a space of 48 meters.

a) What is the acceleration of the cheetah?

b) how long does it take the cheetah to reach a top speed?

Answer 1

The first thing to look for is what you know, and that is the cheetah's

1. initial speed (V₀ = 0)
2. final speed (V_f = 20)
3. distance it travels (d = 48).

For part a, we want to use an equation that only has those variables and the acceleration because that is what we are solving for. Our best equation is:

V_f² = V₀² + 2ad

With this, we solve for the acceleration. I recommend only plugging in values that are zero until you have a final equation. It is a good habit to get into, and it makes everything easier. (You can also then use the final equation if you have the same situation)

V_f² = 0 + 2ad

(V_f²) ⁄ (2d) = a

20² / (2*48) = a = 400/96

a = 25/6 m/s²

Solving for the time, we want to use an equation that has time in it. There are two options

1. d = V₀ t + (1/2) a t²
2. V_f = V₀ + 2ad

The second one is better in my opinion because you don't need to worry about doing a square root, but both work. I'll show both to be thorough, but equation 2 is easier, in my opinion.

1. 1 d = V₀ t + (1/2) a t²

d = 0 + (1/2) a t²

(2d)/a = t²

t = sqrt[(2d)/a]

t = sqrt[96/ (25/6)]

t = sqrt (576/25)

t = 24/5 s = 4.8 s

1. 2 V_f = V₀ + at

V_f = 0 + at

V_f / a = t

20 / (25/6) = t

120/25 = t

24/5 seconds = 4.8 seconds = t

Both options get the same answer. I hope this helps.

Answer 2

a) What is the acceleration of the cheetah?

You want to use x = 48 = v₀t + ½at² = 0 + ½at², but you don't know t.

There are two ways to get around this problem.

1. Find t using x = 48 = ½(v₀ + v)t = ½(20)t = 10t, then plug t =4.8 into 48 = ½at²
2. Find your answer in one step using v² – (v₀)² = v² = 2ax. So (20)² = 2a(48)

Either way you get the same answer

The 1^st way: 48 = ½at² = ½a(4.8)² means that a = 96/(4.8)² =

The 2^nd way: (20)² = 2a(48) = 96a means that a = 400/96 =

(The two formulas above to calculate a might look different but the produce the same number.)

Although the 2^nd way has the advantage of getting there in one step, the 1^st way solves part b en route to answering part a!

b) how long does it take the cheetah to reach a top speed?

48 = ½(v₀ + v)t = ½(20)t = 10t and shown above

so t = 4.8 s