How do you find distance when given acceleration and time

A deer mass 80 kg is running with uniform velocity 72 km/h. In the mean time a tiger of mass 200 kg which was hiding behind a tree started chasing the deer from 75m behind with uniform acceleration 1.5 ms⁻² for 30s.

A. Find the kinetic energy of the tiger after 10s.
B. Is it possible for the tiger to catch the deer? Give your opinion with mathematical analysis.

Solution:

A)

To find the kinetic energy of the tiger after 10 seconds, we need to first determine its velocity at that time. We can use the following kinematic equation to do so:

v = u + at

where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time.

initial velocity of tiger = 0
acceleration of tiger = 1.5ms⁻²

v = u + at
v = 0 + 1.5 x 10
v = 15 m/s

We know,

KE = (1/2)mv²

= 0.5 × 200 × 15²
= 22,500 J

Therefore, the kinetic energy of the tiger after 10 seconds of chasing the deer is 22,500 joules.

B)

the velocity of deer,

v = 72km/h

=72×1000/3600 ms⁻¹

=20 ms⁻¹

distance moved by deer in 30 sec

S₁ =v×t

= 20×30 =600m

Again for tiger,

Initial velocity, u=0

acceleration, a = 1.5ms⁻²

Time, t = 30 sec

So, distance moved by tiger to catch deer in 30 sec is,
S₂ = ut + at²

=0 × 30 + 1.5 × 30²

= 675 m.

As the tiger started casing the deer from 75 m behind.

So, S₂-S₁= (675-600) m = 75 m

It is possible for the tiger to catch deer.