Question

a motorboat starting from rest on a lake accelerates in a straight line at a constant rate of 3 ms-2 for 8s. how far the boat travel during the time​

Answer 1

Given :-

A motorboat starting from rest on a lake accelerates in a straight line at a constant rate of 3 m/s² for 8 seconds .

Required to find :-

• Distance travelled during the time ?

Equations used :-

v = u + at

v² - u² = 2as

Solution :-

Given data :-

A motorboat starting from rest on a lake accelerates in a straight line at a constant rate of 3 m/s² for 8 seconds .

we need to find the distance travelled in that given time ?

So,

From the given information we can conclude that ;

Initial velocity of the motorboat ( u ) = 0 m/s

Acceleration ( a ) = 3 m/s²

Time ( t ) = 8 seconds

using the 1st equation of motion

☛ v = u + at

☛ v = 0 + 3 x 8

☛ v = 0 + 24

☛ v = 24 m/s

Hence,

Final velocity of the motorboat ( v ) = 24 m/s

Using the equation of motion

i.e.

☛ v² - u² = 2as

☛ ( 24 )² - ( 0 )² = 2 x 3 x s

☛ 576 - 0 = 2 x 3s

☛ 576 = 6s

☛ 6s = 576

☛ s = 576/6

☛ s = 96 meters

As we know that

s = displacement

However,

Since, according to the condition we can take displacement in terms of distance but we can't take distance in terms of displacement .

So,

Distance travelled by the motorboat ( s ) = 96 meters

Additional Information :-

These equations of motion are only applicable when the acceleration of the body is constant .

The other equation of motion is ;

• s = ut + ½ at²

Speed is a scalar quantity .

Velocity is a vector quantity .

Answer 2

Given,

u=0,

a=3m/s²,

t=8s

From the formula v=u+at

v=0+8×3

v=24m/s

From the formula s=ut+1/2at²

s=0×8+1/2×3×8²

s=0+3×32

s=96m

HOPE IT HELPS YOU....