Question #0cdf5

2 Answers
Jul 11, 2016

(b) is 12.9s (c) is 66.2m/s and (d) is 24.2s (total time)

Explanation:

The question tells us that the car reaches 60mph from rest after 5.2s, hence the driver will be accelerating for this time (5.2s).

At this point it is useful to covert this speed into SI units:
60 times 1600/3600=26.67ms^-1

So acceleration =(v-u)/t=(26.67-0)/5.2=5.13ms^-2

Whilst decelerating from the top speed to rest we are told that a=-0.6g=-5.88ms^-2

For both phases of travel we can use v^2=u^2+2as
We can define the distance whilst accelerating as s and whilst decelerating as s'

When accelerating from rest:
v^2=0+2*5.13*s
v^2=10.26s

And when decelerating to rest:
0=u^2-2*5.88s'
u^2=11.76s'

Since final velocity for accelerating phase (v)= initial velocity for decelerating phase (u), then
10.26s=11.76s'

And we also know that s+s'=800

Solving:
10.26s=11.76*(800-s)
22.02s=9408

s=427.2m and s'=372.8m

For (b) we can now use s=ut+1/2at^2

427.2=+1/2*5.13t^2
t=12.9s

For (c) top speed is given by v=u+at
v=0+(5.13times12.9)=66.2ms^-1

For (d), the time decelerating we can use s=1/2(u+v)*t

372.8=1/2(66.2+0)*t
t=11.3s

So total time = 11.3+12.9=24.2s

Jul 12, 2016
  1. First step: Acceleration for the car is given for speed from 0" to "60 mph. It is assumed that it can not go above this maximum speed.
    Let us assume that the driver initially accelerates the car for achieving maximum speed. Converting mph to fps 60mph=(60xx1760xx3)/3600=88fts^-1 and taking g=32fts^-2 (all quantities rounded to one place of decimal).
    Acceleration of the car during this period
    v=u+at
    88=0+axx5.2
    a=88/5.2fts^-2
    Distance moved during this acceleration period
    s_a=ut+1/2at^2
    s_a=1/2xx88/5.2xx(5.2)^2
    s_a=228.8ft

  2. Second step: Test run is given as half mile. Balance distance of test run
    s_b=2640-228.8=2411.2ft
    Deceleration is given as 0.6g=0.6xx32=19.2ft s^-2
    Suppose the car is retarded as given and comes to halt. Using the kinematic equation the distance moved s_d is
    v^2-u^2=2as
    0^2-88^2=2xx(-19.2)xxs_d
    s_d=88^2/(2xx19.2)=201.7ft
    Time taken for this part of test run
    v=u+at
    0=88+(-19.2)xxt_d
    =>t_d=88/19.2=4.6s

  3. We see that there is still some distance to be covered for the test run. This distance s_t needs to be covered at the top speed. We know that
    s_t=s_b-201.7=2411.2-201.7=2209.5ft
    Time taken to cover this distance=2209.5/88=25.1s

(a)
my comp.
(b) 5.2s
(c) 88fts^-1
(d) Time of test run =5.2+25.1+4.6=34.9s