
The velocity at time
is

Take two vectors that point in the positive
and positive
directions, such as
and
. The dot products of the velocity vector with
and
are

and

We want the angles between these vectors to be 45º, for which we have
. So



When
, the velocity vector is equal to the zero vector, which technically has no direction/doesn't make an angle with any other vector. So the only time this happens is for

The work done by the man pushing the car over the given distance is 1000J.
Given the data in the question;
- Mass of car;

- Acceleration of the car;

- Distance covered by the car;

Work done;
<h3>Work done</h3>
Work done is simply defined as the energy transfer that takes place when an object is either pushed or pulled over a certain distance by an external force. It is expressed as;

Where f is force applied and d is distance travelled.
To determine the work done by the man, we first solve for the force applied F.
From Newton's Second Law; 
We substitute our given values into the expression

Next we substitute our values into the expression of work done above.

Therefore, the work done by the man pushing the car over the given distance is 1000J.
Learn more about work done: brainly.com/question/26115962
Answer:
i think number 4 :/ i hope its right...
Answer:
t = 4.58 s
Explanation:
In this problem, we need to find the time elapse between seeing lightning and hearing the thunder if the lightning strikes 1mi (5280 ft) away and the air temperature is 90.0°F.
T = 90.0°F = 32.2 °C
The speed of sound at temperature T is given by :
v = (331.3 +0.6T)
Put T = 32.2°C
So,
v = (331.3 +0.6(32.2))
= 350.62 m/s
We have, distance, d = 1 mile = 1609.34
So,

So, the required time is equal to 4.58 seconds.
The magnitude of the induced emf is given by:
ℰ = |Δφ/Δt|
ℰ = emf, Δφ = change in magnetic flux, Δt = elapsed time
The magnetic field is perpendicular to the loop, so the magnetic flux φ is given by:
φ = BA
B = magnetic field strength, A = loop area
The area of the loop A is given by:
A = πr²
r = loop radius
Make a substitution:
φ = B2πr²
Since the strength of the magnetic field is changing while the radius of the loop isn't changing, the change in magnetic flux Δφ is given by:
Δφ = ΔB2πr²
ΔB = change in magnetic field strength
Make another substitution:
ℰ = |ΔB2πr²/Δt|
Given values:
ΔB = 0.20T - 0.40T = -0.20T, r = 0.50m, Δt = 2.5s
Plug in and solve for ℰ:
ℰ = |(-0.20)(2π)(0.50)²/2.5|
ℰ = 0.13V