Question

a car starts from rest and accelerates at a uniform rate of 5 metre per second square for 20 seconds then it travels with a uniform speed for another 10 second then the brakes are applied for car comes to rest after 5 seconds calculate the total distance travelled by the car
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Answer 1

plz refer to the attachment above

Answer = 2250 m

Answer 2

Given

A car starts from rest and accelerates at a uniform rate of 5 m/s square for 20 seconds then it travels with a uniform speed for another 10 second then the brakes are applied for car comes to rest after 5 seconds

To Find

Total distance traveled by the car

Concept Used

As the acceleration is constant throughout the motion , so we need to apply equations of motion ,

$\bf \pink{\bigstar\ \; v=u+at}\\\\\bf \green{\bigstar\ \; s=ut+\dfrac{1}{2}at^2}\\\\\bf \blue{\bigstar\ \; v^2-u^2=2as}$

where ,

• v denotes final velocity
• u denotes initial velocity
• a denotes acceleration
• t denotes time
• s denotes distance traveled

Solution

Here three situations are given ,

Situation - 1 :

• u = 0 m/s

starts from rest

• a = 5 m/s²
• t = 20 s

Apply 2nd equation of motion ,

⇒ s = ut + ¹/₂ at²

⇒ s = (0)(20) + ¹/₂(5)(20)²

⇒ s = 1000 m

Apply 1st equation of motion ,

⇒ v = u + at

⇒ v = (0) + (5)(20)

⇒ v = 100 m/s

This is the initial velocity of the second situation .

Situation - 2 :

• u = 100 m/s
• v = 100 m/s

Uniform speed

• t = 10 s

Apply 1st equation of motion ,

⇒ v = u + at

⇒ (100) = (100) + a(10)

⇒ 10a = 0

⇒ a = 0 m/s²

Apply 2nd equation of motion ,

⇒ s = ut + ¹/₂ at²

⇒ s' = (100)(10) + ¹/₂(0)(10)²

⇒ s' = 1000 m

Situation - 3 :

• u = 100 m/s

constant velocity

• v = 0 m/s

finally went to rest

• t = 5 s

Apply 1st equation of motion ,

⇒ v = u + at

⇒ (0) = (100) + a(5)

⇒ 5a = - 100

⇒ a = -20 m/s²

Note : - ve sign of acceleration denotes retardation

Apply 2nd equation of motion ,

⇒ s = ut + ¹/₂ at²

⇒ s" = (100)(5) + ¹/₂ (-20)(5²)

⇒ s" = 500 - (10)(25)

⇒ s" = 500 - 250

⇒ s" = 250 m

So , Total distance traveled ,

D = s + s' + s"

⇒ D = 1000 + 1000 + 250

⇒ D = 2250 m