Simple Normal/Tangential Acceleration Confirmation Needed

[Griffy11]

Hi guys,

Got an exam this afternoon, and really need help with this. I think I'm right, but I just need verification and explanation.

Homework Statement

A car rounds a bend with a radius of 200m. At a particular instant, the car has a velocity of 60km/h. The speed of the car is increasing at a rate of 5m/s^2. Determine:

i) the normal and tangential components of the acceleration of the car
ii) the magnitude and direction of the resultant acceleration
iii) how far around the ben dthe car will travel before v=20m/s

Homework Equations

at = the rate at which v increases, given as 5m/s^2 in the question.
an = v^2/r

The Attempt at a Solution

My solutions:
i) an=v^2/r=((60/3.6)^2)/(200) = 1.38m/s^2
at = 5m/s^2

ii) |a| = sqrt(1.38^2+5^2) = 5.186m/s^2
theta = tan^-1(an/at) = tan^-1(1.38/5) = 15.43 degrees

iii) No idea. Really need help with this one.

Are i and ii correct? Help with iii appreciated also. Thank you so much.

 

[LawrenceC]

i) an=v^2/r=((60/3.6)^2)/(200) = 1.38m/s^2



For the final part think about the equations for uniformly accelerating bodies.