Question

A certain drag racer can accelerate from 0 to 90 km/h in 5.0 s. (a) What is its average acceleration, in g’s, during this time? (b) How far will it travel during the 5.0 s, assuming its acceleration to be constant? (c) How much time would be required to go a distance of 0.5 km if the acceleration could be maintained at the same value?

Answer 1

Hello Dear.

Here is the answer---


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Given Conditions,

  Initial Velocity(u) = 0
 Final Velocity(v) = 90 km/hr.
                             = 90 × (5/18)  [Changing into m/s]
                             = 25 m/s.

  Time(t) = 5 seconds.

(a)  Using the Formula,

  Acceleration = (v - u)/t
                       = (25 - 0)/5
                       = 25/5
                       = 5 m/s².
 
For Changing into g(acceleration due to gravity0
 
      ∵   9.8 m/s² is equal to g.
      ∴   1 m/s² ----------------g/9.8
    ∴  5 m/s²-----------------(g/9.8) × 5
                                          = 0.51 g

Where g is the acceleration due to gravity.

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(b) 
 For the Distance,
     Time(t) = 5 seconds.
    Speed = 90 km/hr. [Since, the acceleration is constant]
               = 25 m/s.   [Changing into m/s]

Using the Formula,
   
   Speed = Distance/Time
   ⇒ Distance = Speed × Time
                      = 25 × 5
                      = 125 m.

Thus, the Distance traveled by the drag racer in 5 seconds is 125 m.

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(c) Given, Distance = 0.5 km
                               = 500 m.
   
    Speed = 90 km/hr.   [Since the acceleration is constant]
               = 25 m/s   [Changing into m/s]

Thus, Time = Distance/Speed
                   = 500/25
                  = 20 seconds.

Time taken by the Drag racer to cover the distance of 0.5 km (500 m) is 20 seconds.

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Hope it helps.

Have a Marvelous Day.