Could anyone please help me with part F?

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2 Answers
Jun 9, 2018

Please see the explanation below.

Explanation:

The velocity is constant at #t_2=30s#

#(ds)/dt=60kmh^-1#

Therefore,

The acceleration is

#a=(d^2s)/dt^2=d/dt((ds)/dt)=0ms^-2#

Jun 9, 2018

The instantaneous acceleration at #t_2= 30# sec. is
#a_2=-10/6 m/s^2 ~~ -1.67 m/s^2#

Explanation:

According to the figure we have a constant speed until 30 sec, at which point the movement descelerates, so that the speed changes constantly from 60 km/h to 0 km/h in 10 sec. (from 30 to 40 sec.).

Acceleration is speed change per second, i.e. #(Deltav)/(Delta t)#

We, therefore need to convert the speed from #(km)/h# to #m/s#

#60 (km)/h=60000/3600 m/s=100/6 m/s#

(60 km = 60 000 m, and there are 3600 sec. in 1 hour)

Therefore #a=(Deltav)/(Delta t)#
#=(0-100/6)/10 m/s^2#
#=-10/6 m/s^2=-1.67 m/s^2#

The figure shows that the acceleration is constant from 30 to 40 sec. The instantaneous acceleration at #t_2= 30 s#, therefore, is
#a_2=-10/6 m/s^2 ~~ -1.67 m/s^2#