Question

A car starting from rest, accelerates at the rate f through a distance S, then
continues at constant speed for time t and then decelerates at the rate f/2 to
come to rest. If the total distance transferred is 5 &, then
1
(a) S= ft
(b) S=ft2
(c) S=f2 (d) S= 12​

Answer 1

Answer:

If t

1

be the time for which the car accelerates at the rate f from rest, the distance traveled in time t

1

is

s=s

1

=0(t

1

)+

2

1

ft

1

2

=

2

1

ft

1

2

....(1) (using formula

s=ut+

2

1

at

2

)

and the velocity at time t

1

is v

1

=ft

1

So, the distance traveled in time t will be s

2

=v

1

t=ft

1

t ...(2)

If t

2

be the time for which the car decelerates at the rate f/2 to come rest, the distance traveled in time t

2

is given by,

0

2

−v

1

2

=2(−f/2)s

3

(using formula v

2

−u

2

=2as)

or s

3

=(ft

1

)

2

/f=ft

1

2

...(3)

using (1), s

3

=2s

1

=2s

Given, s

1

+s

2

+s

3

=15s

or s+ft

1

t+2s=15s

or ftt

1

=12s

or 12s=ftt

1

..(4)

(4)/(1)⇒

s

12s

=

(1/2)ft

1

2

ftt

1

or t

1

=t/6

From (1), s=(1/2)f(t/6)

2

=ft

2

/72

Answer 2

Answer:

If t

1

be the time for which the car accelerates at the rate f from rest, the distance traveled in time t

1

is

s=s

1

=0(t

1

)+

2

1

ft

1

2

=

2

1

ft

1

2

....(1) (using formula

s=ut+

2

1

at

2

)

and the velocity at time t

1

is v

1

=ft

1

So, the distance traveled in time t will be s

2

=v

1

t=ft

1

t ...(2)

If t

2

be the time for which the car decelerates at the rate f/2 to come rest, the distance traveled in time t

2

is given by,

0

2

−v

1

2

=2(−f/2)s

3

s=f2

Explanation:

If t

1

be the time for which the car accelerates at the rate f from rest, the distance traveled in time t

1

is

s=s

1

=0(t

1

)+

2

1

ft

1

2

=

2

1

ft

1

2

....(1) (using formula

s=ut+

2

1

at

2

)

and the velocity at time t

1

is v

1

=ft

1

So, the distance traveled in time t will be s

2

=v

1

t=ft

1

t ...(2)

If t

2

be the time for which the car decelerates at the rate f/2 to come rest, the distance traveled in time t

2

is given by,

0

2

−v

1

2

=2(−f/2)s

3

(using formula v

2

−u

2

=2as)

or s

3

=(ft

1

)

2

/f=ft

1

2

...(3)

using (1), s

3

=2s

1

=2s

Given, s

1

+s

2

+s

3

=15s

or s+ft

1

t+2s=15s

or ftt

1

=12s

or 12s=ftt

1

..(4)

(4)/(1)⇒

s

12s

=

(1/2)ft

1

2

ftt

1

or t

1

=t/6

From (1), s=(1/2)f(t/6)

2

=ft

2

/72