Question

A toy car starts from rest and accelerates on a straight road at a rate of 3m/s^2 for 5 seconds. In the next 2 seconds, it continues to move at a constant speed. Finally, it accelerates at a rate of 2m/s^2 until it stops in the rest of the rest of the time. Find its

a.) Displacement

b.) Speed at t=6 seconds

c.) plot the following graphs:

I. x vs. t

II. v vs. t

III. a vs. t

Answer 1

We know the equations of motion

   ............................(1)

   ..............................(2)

...........................(3)

Where, u is initial velocity

v is final velocity

S is total displacement  

a is acceleration of the object

t is time of motion

As the toy car starts from rest and accelerates at a rate of 3m/s² for 5 seconds then after 5 seconds ,

velocity of the car is

(used equation 1)

total displacement of the car is

(used equation 3)

For next 2 seconds it moves with constant velocity . So,

velocity of the car after 7 seconds is

(as velocity is constant)

total displacement of the car in these 2 seconds is

  

So, total displacement of the car after 7 seconds is

.

Finally it de-accelerated at a rate of 2 m/s² until it stops.

Applying equation 1 in this intervel of time , we get

   (as the car finally stops)

or,  

Applying equation (2), we get

or,   

So, total time of motion = 5 + 2 + t₃ = 7 + 7.5 = 14.5 s

And the total displacement of car afte 14.5 seconds is = S₁ + S₂ + S₃ = 67.5 + 56.25 = 123.75 m

(a) Total displacement of the car is 123.75 m .

(b) Speed of the car at t = 6 seconds was 15 m/s .

(c)

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