Question

How much distance will a vehicle moving with uniform acceleration of 4m/s2 cover in 5 seconds if the initial velocity of the vehicle is 5m/s.
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Answer 1

Given

Uniform acceleration = 4m/s²

Time given = 5 seconds.

Initial velocity of vehicle = 5 m/s

To Find

Distance travelled by the vehicle.

Solution

Here, u = 5 m/s, vehicle moving with uniform acceleration of 4 m/s² .It will cover s distance in 5 seconds.

We know equation of motion :

➝ s = ut + ½at²

Putting all values we get :

➝ s = 5(5) + ½(4 × 5²)

➝ s = 25 + ½(4 × 25)

➝ s = 25 + ½(100)

➝ s = 25 + 50

➝ s = 75 m

Therefore,

Distance covered by vehicle is 75 m.

________________________

More such equation of motions :

➥ v = u + at

➥ v² - u² = 2as

➥ a = (v - u)/t

Answer 2

Given :-

Acceleration(a) of the vehicle is 4 m/s².

Time taken(t) = 5 s

Initial velocity of the vehicle = 5 m/s

To find :-

The distance covered by the vehicle.

Solution :-

Method 1 :-

We know,

$\displaystyle{\sf{v=u+at}}\\\\\text{Putting all the known values :}\\\displaystyle{\sf{\implies v=5+(4*5)}}\\\\\displaystyle{\sf{\implies v=5+20}}$

$\bold{ \displaystyle{\sf{\: \implies v=25\ m/s}}}$

Now, we also know,

$\displaystyle{\sf{v^2-u^2=2as}}$

$\text{Putting all the known values :}$

$\displaystyle{\sf{(25)^2-(5)^2=2*4*s}}\\\\\displaystyle{\sf{\implies 625-25=8s}}\\\\\displaystyle{\sf{\implies s=\frac{600}{8} }}\\\\\\\displaystyle{\sf{\boxed{\implies s=75\ m}}}$

Method 2 :-

We know,

$\displaystyle{\sf{s=ut+\frac{1}{2}at^2 }}\\\\\text{Putting all the known values :}\\\\\displaystyle{\sf{\implies s=5*5+\frac{1}{2}*4*(5)^2 }}\\\\\displaystyle{\sf{\implies s=25+2*25}}\\\\\displaystyle{\sf{\implies s=25+50}}\\\\\displaystyle{\sf{\boxed{\implies s=75\ m}}}$

So, the distance covered by the vehicle is 75 m.