Question

If an automobile’s braking distance from 90 km/h is 45 m on level pavement, determine the automobile’s braking distance from 90 km/h when it is going up a 5° incline. Please show your work by including the FBD & KD.

Problem #2 If an automobile's braking distance from 90 km/h is 45 m on level pavement, determine the automobile's braking distance from 90 km/h when it is going up a 5° incline. Please show your work by including the FBD & KD

Answer 1

given is

the velocity of automobile u = 90km/hr = 25 m/s

braking distance on level pavement S = 45 m

from the equation of motion

V2 = U2 - 2*a*S

0 = 252 - 2*a*45

a = 625/90 = 6.94 m/s2

now the automobile is going up an incline of 5o with 25 m/s

the free body diagram of automobile is shown below.

mg sin(5) mg cos(5) V mg

thus the net deceleration rate = a + g sin(5)

= 6.94 + 9.81*sin(5)

= 7.794 m/s2

thus the braking distance can be calculated as

V2 = U2 - 2*a*S

0 = 252 - 2 * 7.794 * S

S = 625/(2*7.794)

= 40.094 m

thus braking distance is 40.094 m