I am unable to get the exact answer to this question: A motorist drives along a

Question

I am unable to get the exact answer to this question:
A motorist drives along a straight road at a constant speed of25.0m/s. Just as she passes a parked motorcycle policeofficer, the officer starts to accelerate at 3.00m/s^2 to overtakeher. Assume that the officer maintains thisacceleration.
a) Determine the time it takes the police officer to reach themotorist b) Find the speed of the officer as he overtakes themotorist c) Find the total displacement of the officer as he overtakesthe moterist
Thank you.
A motorist drives along a straight road at a constant speed of25.0m/s. Just as she passes a parked motorcycle policeofficer, the officer starts to accelerate at 3.00m/s^2 to overtakeher. Assume that the officer maintains thisacceleration.
a) Determine the time it takes the police officer to reach themotorist b) Find the speed of the officer as he overtakes themotorist c) Find the total displacement of the officer as he overtakesthe moterist
Thank you.

Explanation / Answer

   Let the police officer takes t s to overtakethe motorist. a.     Distance travelled bymotorist in ts         d1   =   speed* t   =   25.0 *t      m    Distance travelled by police officer in ts      d2   =   u* t   +   (1/2) * a *t2    u   =   initialspeed of policeofficer   =   0,   a   =   acceleration   =   3.00   m/s2       d2   =   0* t   +   0.5 * 3.00 *t2   =   1.50 *t2    When the police officer overtakes themotorist,   d1   =   d2    =>   1.50 *t2   =   25.0 *t            or            t   =   25.0/ 1.50   =   16.67   s    b.   Speed of officer isgiven by first equation       v   =   u+ a *t   =   0   +   3.00* 16.67   =   50.00   m/s    c.   distance travelled bypolice officer   d2   =   1.5* t2   =   1.5 *16.672   =   416.83   m    =>   1.50 *t2   =   25.0 *t            or            t   =   25.0/ 1.50   =   16.67   s    b.   Speed of officer isgiven by first equation       v   =   u+ a *t   =   0   +   3.00* 16.67   =   50.00   m/s    c.   distance travelled bypolice officer   d2   =   1.5* t2   =   1.5 *16.672   =   416.83   m

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