can u please show me how to do this with clear steps thank u 6) Spike Witwicky i

Question

can u please show me how to do this with clear steps thank u

6) Spike Witwicky is driving his car with a constant velocity of 35 m/s and passes a state trooper. 5 sec later the trooper accelerates at 5 m/s? a) First, what kind of car is Spike driving? (1 pt) b) How much time does the trooper need to catch up to Spike? (9 pts) c) How fast is each car moving when the trooper catches Spike? (9 pts) d) How far did the trooper drive to catch Spike? (8 pts) e) What are the trooper and Spikes average speeds and velocities? (8 pts) Vf mls

Explanation / Answer

Given car is driven with constant velocity U = 35m/s and passes a trooper . the trooper starts after 5 seconds with a acceleration a = 5m/s^2

b) time neede by trooper to catch up to spike.

let t be the the time taken by the trooper to catch up with spike after spike crosses the trooper. as the trooper acclerates after 5 seconds , trooper maintains acceleration for ( t-5) seconds.

So distance travelled by spike in t seconds is equal to distance travellrd by trooper in t-5 seconds with acceleration 5 m/s^

Distance travelled by spike in t seconds Ds = U1. t

U1 =35 m/s

Ds = 35 t

Distance travelled by trooper in t sec Dt =U2 .t+ 0.5 a T^2

   U2=0 as initial velocity of trooper is zero. a=5m/s^2 T=t-5

   Dt = 0.5 *5* (t-5 )^2

   Dt = 2.5 (t^2 + 25 -10t)

Ds =Dt

35t= 2.5 (t^2+25-10t)

70t=5t^2-50t +125

5t^2-120t+125=0

t^2-24t+25=0

   t= 22.9 sec or 2.2 sec

t can not be 2.2 sec because trooper is at rest for 5 sec after spike crossed trooper so

t=22.9 sec nearly 23 sec

c) velocity of spike car after trooper catching upto spike is 35 m/s as spike is moving with constant velocity.

   velocity of trooper after 22.9 sec Vt =Ut+at =0+ 5(22.9) = 114.5 m/s

d) distance trooper has to drive to catch upto spike =Dt =Ds =Us.t= 35*22.9 =801.5 m

e) average speed is ratio total distance to total time taken to travel the distance

   average velocity is the ratio of total displacement to time taken for the displacement

1.Average speed and average velocity of spike car is same as it is moving at constant velocity=35m/s

2 average speed of trooper car =total distance /total timeto cover the distance

= 801.5(22.9-5)    as trooper started 5 seconds late

   =801.5/17.9=44.77 m/s

Average velocity = total displacement/ total time for displacement =114.5/22.9 =35 m/s

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